Question

When dividing the complex numbers, the first step is to multiply top and bottom by the complex _____ f the denominator.
Is the correct answer conjugate?

Answer 1

Yep :)

Answer 2

Thank you so much!:)

Answer 3

No problem. Easiest "help" I've ever given!

Answer 4

Could you help me with one more thing?:)

Answer 5

\[\frac{ 2+3i }{ 1+2i }\]

Answer 6

Ok. What's the conjugate of the denominator?

Answer 7

2??

Answer 8

When we take a complex conjugate, we just change the sign in front of everything with an "i"

\[(a+b+c+di)^* = (a+b+c-di)\]

Answer 9

oh yes! Okay I remember now.. Got it.

Answer 10

So from there what would I do?

Answer 11

Multiply both the top and the bottom by the conjugate of the denominator

Answer 12

It should look like:
\[\frac{2+3i}{1+2i}\frac{1-2i}{1-2i} = ?\]

Answer 13

\[\frac{ -4-i }{ 3}\]

Answer 14

Isn't that the final answer?

Answer 15

That's not what I get. Let me double check mine

Answer 16

wait! no it's over 5!

Answer 17

Closer to what I get :)

Answer 18

(2+3i)(1-2i) = 2*1+3i*1+2*(-2i) + 3i*(-2i)

Answer 19

Oh, I see what happened on yours. 3i * -2i = -6*i^2 = 6

Answer 20

The denominator is 5 isn't it?

Answer 21

Yeah

Answer 22

Okay got it.. Thought so.

Answer 23

What is your final answer? Your numerator wasn't quite correct, before.

Answer 24

Wait wait wait! is the top 8-i!?

Answer 25

There you go :)

Answer 26

\[\frac{ 8-i }{ 5 }\]

Answer 27

That's what I get :)

Good work!

Answer 28

Thank you so much for all the help!

Answer 29

My pleasure. Keep up the good work!