Question

1+ i : write the complex number in polar form with argument theta between 0 an 2 pi.... I know the answer but i need help getting to it

Answer 1

What did you have for an answer? And have you tried anything in particular so far?

Answer 2

We want to find polar form, which is a combination of a 'radius'/magnitude and angle from the terminal axis (the positive real line).
We currently know its rectangular equivalent is z = 1 + i .

Answer 3

I found out how.. now im just stuck on another problem

Answer 4

Oh, alright. If you require assistance on it, feel free to post the problem here. :p

Answer 5

haha okay i need help writing 2 sqrt 3 - 2i in polar form

Answer 6

i have the argument down but i do not know how to square the 4 radical 3

Answer 7

As in: \( r = \left( 2 \sqrt{3} \right)^2 + 2^2\) ?

Answer 8

yes!

Answer 9

You could use the property of exponents of distributing to each factor:
\(\left(ab \right)^x = a^x b^x \)
\( \left(2 \sqrt{3} \right)^2 = 2^2 \left(\sqrt{3}\right)^2 \)
Does that help?

Answer 10

oh wait 12

Answer 11

Yeah. The square and square root cancel. :)

Answer 12

but the answer says it is \[4( \cos 11\pi/6 + i \sin 11\pi/6)\]

Answer 13

Oops, I made a small mistake above with that radius formula:
\( r^{\color{red}2} = \left(2\sqrt{3}\right)^2 + 2^2 \)

Answer 14

r^2 = 12 + 4 = 16
so r = sqrt(16) or 4.

Answer 15

oh wow okay!!

Answer 16

thank you

Answer 17

Yep, you're welcome! :)