Question

Help me on how to solve these questions with complex numbers: a) 2-i / sqrt2 - i ; b) 3 + 4i / 4 - 3i ; c) 3 / 1 + i ; d) 4i / 2 - 3i

Answer 1

if you have A/B where B is complex, multiply top and bottom by the complex conjugate of B

\[ \frac{A}{B} \cdot \frac{B^*}{B^*} \]

Answer 2

I only have one question. With the square root though, how do I simplify that?

Answer 3

you don't.
for (a) you have
\[ \frac{2-i}{\sqrt{2}-i}\cdot \frac{\sqrt{2}+i}{\sqrt{2}+i} \\
\frac{(2-i)( \sqrt{2}+i)}{2-i^2}\\
\frac{(2\sqrt{2}+1) +(2-\sqrt{2})i}{3}
\]

Answer 4

okay thanks. Also, I got the answer -10/25 + i for b) but I don't think it's the correct solution.

Answer 5

how ?

Answer 6

I have my insecurities, haha I just want to make sure I understand complex numbers since I have a test next week.

Answer 7

how did you get your answer for (b)? It looks wrong.

Answer 8

The complex conjugate. I must have done something wrong in the second last or last step.

Answer 9

the bottom is 25

what do you get for the top.... can you show the details as you multiply
(3 + 4i ) * (4 + 3i )

Answer 10

first step