حمّل تطبيق منهاجي الجديد

منهاجي صار أسرع من خلال التطبيق
  أتحقق من فهمي

أتحقق من فهمي

الأعداد المركبة

الوحدة التخيلية والعدد التخيلي

أتحقق من فهمي صفحة 141

أجد قيمة الجذر الرئيس في كلّ ممّا يأتي بدلالة i :

(a) square root of negative 75 end root

begin mathsize 20px style square root of negative 75 end root equals square root of negative 1 cross times 25 cross times 3 end root equals square root of negative 1 end root cross times square root of 25 cross times square root of 3 equals 5 i square root of 3 end style

(b) square root of negative 49 end root

begin mathsize 20px style square root of negative 49 end root equals square root of negative 1 cross times 49 end root equals square root of negative 1 end root cross times square root of 49 equals 7 i end style

 

ضرب الأعداد التخيلية

أتحقق من فهمي صفحة 142

أجد ناتج كلّ ممّا يأتي في أبسط صورة مفترضاً أنّ  :

(a) begin mathsize 20px style square root of negative 27 end root cross times square root of negative 48 end root end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell square root of negative 27 end root cross times square root of negative 48 end root end cell cell equals square root of negative 1 cross times 27 end root cross times square root of negative 1 cross times 48 end root end cell row blank cell equals i square root of 9 cross times 3 end root cross times i square root of 16 cross times 3 end root end cell row blank cell equals i squared square root of 9 cross times 3 cross times 16 cross times 3 end root end cell row blank cell equals 36 i squared equals negative 36 end cell end table end style

(b) begin mathsize 20px style square root of negative 50 end root cross times negative 4 i end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell square root of negative 50 end root cross times negative 4 i end cell cell equals square root of negative 1 cross times 50 end root cross times left parenthesis negative 4 i right parenthesis end cell row blank cell equals 5 i square root of 2 cross times left parenthesis negative 4 i right parenthesis equals negative 20 square root of 2 i squared equals 20 square root of 2 end cell end table end style

(c) begin mathsize 20px style i to the power of 2021 end style

begin mathsize 20px style i to the power of 2021 equals left parenthesis i squared right parenthesis to the power of 1010 cross times i equals left parenthesis negative 1 right parenthesis to the power of 1010 cross times i equals i end style

 

خاصية المساواة للأعداد المركبة

أتحقق من فهمي صفحة 144

أجد قيمة x ، وقيمة y الحقيقيتين اللتين تجعلان المعادلة: begin mathsize 20px style x plus 5 plus left parenthesis 4 y minus 9 right parenthesis i equals 12 minus 5 i end style صحيحة.

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x plus 5 plus left parenthesis 4 y minus 9 right parenthesis i equals 12 minus 5 i end cell cell not stretchy rightwards arrow x plus 5 equals 12 space comma space 4 y minus 9 equals negative 5 end cell row cell not stretchy rightwards arrow x equals 7 space comma space y equals 1 end cell blank end table end style

 

تمثيل العدد المركب ومرافقه بيانياً

أتحقق من فهمي صفحة 145

أمثّل العدد المركب ومرافقه بيانياً في المستوى المركب في كلّ ممّا يأتي:

(a) begin mathsize 20px style z equals 2 plus 7 i end style

begin mathsize 20px style z equals 2 plus 7 i space comma stack space z with not stretchy bar on top equals 2 minus 7 i end style

(b) begin mathsize 20px style z equals negative 3 minus 2 i end style

begin mathsize 20px style z equals negative 3 minus 2 i space comma stack space z with not stretchy bar on top equals negative 3 plus 2 i end style

(c) begin mathsize 20px style z equals negative 3 i end style

begin mathsize 20px style z equals negative 3 i space comma stack space z with not stretchy bar on top equals 3 i end style

 

مقياس العدد المركب

أتحقق من فهمي صفحة 146

أجد مقياس كل عدد مركب ممّا يأتي:

(a) begin mathsize 20px style z equals negative 3 minus 6 i square root of 2 end style

begin mathsize 20px style z equals negative 3 minus 6 i square root of 2 space of 1em not stretchy rightwards arrow vertical line z vertical line equals square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis negative 6 square root of 2 right parenthesis squared end root equals square root of 81 equals 9 end style

(b) begin mathsize 20px style z equals negative 2 i end style

begin mathsize 20px style z equals negative 2 i not stretchy rightwards arrow vertical line z vertical line equals square root of left parenthesis 0 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root equals square root of 4 equals 2 end style

(c) begin mathsize 20px style z equals 4 plus square root of negative 20 end root end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell z equals 4 plus square root of negative 20 end root equals 4 plus square root of negative 1 end root cross times square root of 20 equals 4 plus i square root of 20 end cell row blank cell not stretchy rightwards arrow vertical line z vertical line equals square root of left parenthesis 4 right parenthesis squared plus left parenthesis square root of 20 right parenthesis squared end root equals square root of 36 equals 6 end cell end table end style

 

سعة العدد المركب

أتحقق من فهمي صفحة 150

أجد سعة كل من الأعداد المركبة الآتية مقرباً إجابتي إلى أقرب منزلتين عشريتين:

(a) begin mathsize 20px style z equals 8 plus 2 i end style

Error converting from MathML to accessible text.

(b) begin mathsize 20px style f left parenthesis x right parenthesis equals cube root of x minus 3 end root end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

(c) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

(d) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

 

الصورة المثلثية للعدد المركب

أتحقق من فهمي صفحة 152

أكتب العدد المركب في كلّ ممّا يأتي بالصورة المثلثية:

(a) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

(b) begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

(c) begin mathsize 20px style z equals 2 i end style

begin mathsize 20px style table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row blank cell f to the power of ′′ left parenthesis x right parenthesis equals x e to the power of x plus e to the power of x plus e to the power of x equals e to the power of x left parenthesis x plus 2 right parenthesis end cell row blank cell f to the power of ′′ left parenthesis negative 1 right parenthesis equals e to the power of negative 1 end exponent greater than 0 end cell end table e

إعداد : شبكة منهاجي التعليمية

24 / 11 / 2022

النقاشات