simplify 13/-3+2i

Question

simplify 13/-3+2i

welshfella · Answer

do you know what the conjugate of the complex number in the denominator is?

anonymous · Answer

No, I don't understand this... I tried to solve it but it didn't match any of the answer choices. @welshfella

welshfella · Answer

the conjugate will convert the denominator to a real number
its hase the same 'number' parts as the complex number but a different sign
so her we would multiply the top and bottom of the fraction by the conjugate of 
-3 + 2i which is -3 - 2i

welshfella · Answer

can you try that

anonymous · Answer

Okay let me try... @welshfella

anonymous · Answer

So I got -3-2. Am I right so far? @welshfella

welshfella · Answer

which part of you done  - multiplying the denominator?

anonymous · Answer

I did the top and bottom by -3-2i and I got -3-2. Did I do something wrong? @welshfella

welshfella · Answer

yes looks like you did

the bottom part is
(-3 + 2i)(-3 - 2i) = -3*-3 + -3*-2i  - 3*2i +2i*-2i
                            = 9 +3*2i-3*2i -2i^2
                            = 9 + 4  = 13

welshfella · Answer

note hot the terms in i are eliminated - thats why you multiply by the conjugate

welshfella · Answer

- you distribute -3 over the second bracket then do the same with + 2i

welshfella · Answer

do you follow that ok?