Question

3+2i / 3-2i leave answer in a+bi form

the answer is 5/13 + 12/13i , but i keep getting a different answer please help me!!

Answer 1

so you have
3+2i/3-2i

or do you mean
(3+2i)/(3-2i)?

Answer 2

i think you mean the latter
\[\text{ so we have } \frac{3+2i}{3-2i}\]
do you know to put it in a+bi form
the first step you must take is to multiply both top and bottom by bottom's conjugate

Answer 3

do you know what the conjugate of 3-2i is?

Answer 4

multipy numerator and denominator with 3+2i

Answer 5

@myininaya
yes i multiplied the top and bottom by 3+2i and got

9+6i+6i+4i^2
over
9+6i-6i-4i^2

and got the final answer as 9+12i / 9 but its the wrong answer

Answer 6

so how did you get 9+4i^2 is 9?

Answer 7

recall i^2 is -1

Answer 8

so you got it right so far to say
\[\frac{9+6i+6i+4i^2}{9+6i-6i-4i^2}\]

Answer 9

and you know again i^2 is -1
so you have
\[\frac{9+12i+4(-1)}{9-4(-1)}\]
wherever there was an i^2 i just replaced it with -1

Answer 10

simplify this and you will see you got the answer as it should be written

Answer 11

Thanks so much @myininaya

Answer 12

I think this means you got it
so gj