Question

Please help! In need of assistance!

a)connvert the following expression to polar form and then perform the indicated operations. Express answers in b) polar form and c) rectangular form.

the expression is:
(-1+ i√3) (2 - 2i√3) / (4√3 - 4i)

Answer 1

how far did you get?

Answer 2

Honestly I have no idea on how to start solving the answer. This is one of hard questions that look like none of the other easy ones that I've been able to solve on my own.

Answer 3

Hopefully you agree that something like \(\Large -1+i\sqrt{3}\) is in the form \(\Large a+bi\) ?

Answer 4

It might help to turn \(\Large -1+i\sqrt{3}\) into \(\Large -1+(\sqrt{3})i\)

Answer 5

Yes, complex number are said to be in of z = a + bi if I'm correct.

Answer 6

\(\Large \color{red}{-1}+(\color{red}{\sqrt{3}})i\)

\(\Large \color{red}{a}+\color{red}{b}i\)


We see that
\(\Large a = -1\)
\(\Large b = \sqrt{3}\)

agreed?

Answer 7

yes. So would I take the a and b and subsitute those numbers into the formula of z =r(cos θ + i sin θ) ?

Answer 8

you'll need r and theta. Once you have those two values, you then plug them into what you just typed

Answer 9

\[\Large r = \sqrt{a^2 + b^2}\]


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\[\Large \theta = \arctan\left(\frac{b}{a}\right)\]

(a,b) = (-1,sqrt(3)) is a point in quadrant 2. So whatever result you get for theta above, add pi radians to that result. This is so you move from Q4 to Q2.

Answer 10

Ah... so it's not the right formula that i was looking at. you take the | a + bi| which is equal to the square root a squared + b squared which i equal to square root 2. Then subsitute the answer into tanθ = a/b which is equal to -tan square root 3 which is what I got.

Answer 11

you use arctan, not tan

Answer 12

arctangent = inverse tangent

Answer 13

sorry i meant b / a.

Answer 14

Ok. and when i used that I got -60 which does not seem right to me unless it is.

Answer 15

I think i should be getting it in radians.

Answer 16

-60 degrees = -pi/3 radians

use the equality `pi radians = 180 degrees` to convert

Answer 17

the angle is in Q4

Answer 18

add pi radians to the angle to move it to Q2 where it belongs

Answer 19

and when I did pie + -pie / 3 radians I got 2 pie / 3 radians.

Answer 20

Sorry to be nitpicky, but it's `pi` and NOT `pie`. There is no 'e' in the spelling of the greek letter \(\Large \pi\)

anyways, yes, adding pi to -pi/3 is going to get you 2pi/3. Good

Answer 21

Lol, I'm sorry about that. I'm quite embarrased that yoy picked that out. Thank you.

Answer 22

you*

Answer 23

you should find that r = 2 and theta = 2pi/3

so \[\Large -1+i*\sqrt{3} \ \ \rightarrow \ \ 2\left(\cos\left(\frac{2\pi}{3}\right)+i*\sin\left(\frac{2\pi}{3}\right)\right)\]

Answer 24

The first in \(\Large a+bi\) form. The second in \(\Large r(\cos(\theta)+i*\sin(\theta))\) form.

Answer 25

Follow the same steps for the other two expressions

Answer 26

Thank you very much Mr. Thompson. I was not expecting that you would go through most of the steps with me. I greatly appreciate the time that you have given me to solve this problem alot more easier. I should be able to take it from here. Thank you once again. :)

Answer 27

you're welcome