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Divide - in standard form for complex numbers

 

 

2−3i/−1+5i  =

 Apr 30, 2020
 #1
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To divide two complex numbers, multiply both the numerator and the denominator of the fraction by the

conjugate of the denominator.

 

The conjugate of the complex number  a + bi  is the complex number  a - bi.

 

Denominator:  -1 + 5i     --->     Conjugate:  -1 - 5i

 

[ (2 - 3i) / (-1 + 5i) ]  · [ (-1 - 5i) / (-1 - 5i) ]  =  [ (2 - 3i) · (-1 - 5i) ]  /  [ (-1 + 5i) · (-1 - 5i) ]

 

Now, you'll need to multiply:  (2 - 3i) · (-1 - 5i)          [this will be the numerator of your answer]

and   you'll need to multiply:  (-1 + 5i) · (-1 - 5i)        [this will be the denominator of your answer]

 

The denominator will no longer contain any "i" terms; it will just be a regular, real, number.

 Apr 30, 2020

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