imaginary nubmers and division

Question

 Evaluate the expression−4+3i/4+4i
and write the result in the form a+bi .

The real number a equals
The real number b equals

 

I got a=-1 and b=3/4

The answer I was supposed to get is a=-0.125 and b=0875 however I am not sure which operations I'm missing or not applying to get the correct answer.

Answer 1

Hi Emily, to divide imaginary numbers, you need to multiply the numerator and denominator by the conjugate of the denominator.

 

Setup;

 

(-4+3i)/(4+4i) 

 

Conjugate of the denominator, 4+4i is: 4 - 4i.

 

Multiple both the numerator and denominator by 4 - 4i.

 

((-4+3i) * (4 - 4i)) / ((4 + 4i) * (4 - 4i))

 

Evaluate the denominator first:

 

(4 + 4i) * (4 - 4i) = 16 + 16i - 16i -16i²

                          =  16 + 16

                          =  32

 

The denominator reduces to 32.

 

Evaluate the numerator:

 

(-4+3i) * (4 - 4i) = -16 + 16i +12i - 12i²

                          = -16 + 28i + 12

                          =  -4  + 28i

 

New division:

 

(-4 + 28i) / 32

 

Factor 4 from numerator:

 

4 * (-1 + 7i) / 32

 

Cancel the out the 4:

 

(-1 + 7i) / 8 or -1/8 + 7/8i

 

Last find the a and b values:

 

a = -1/8, or -.125

 

b = 7/8, or .875

 

Questions?

Answer 2

(-4 + 3i) (4 - 4i) = -16 + 28i -12 i²  = -16 + 28i + 12

(4 + 4i)  (4 - 4i)         16 - 16i²                 16 + 16

 

-4 + 28i   = -1/8 + 7/8 i

     32

a = -0.125 and b = 0.875