Question

Can someone please help me finish this pre-calc question???

Express the complex number in trigonometric form.

2 - 2i

This is what I have so far:
r=absolute value(2-2i)
r= sqrt((2)^2+(-2)^2)
r=sqrt(8)
r=2sqrt(2)

theta(ref)=tan^-1*absolute value(2/-2)
theta(ref)=pi/2

I dont know how to get the value of theta alone to complete this problem. What do i do next? Please help!

Answer 1

\[2-2i\]\[r=\sqrt{2^2+(-2)^2}\]\[\tan^{-1} = (\frac{ -2 }{ 2 } ) = ?\]

Answer 2

you arent suppose to use radian mode for polar form

Answer 3

thats why you got pi/2

Answer 4

I thought \[\tan^{-1} =\frac{ a }{ b }\]

Answer 5

no its b/a

Answer 6

better if i draw it out?

Answer 7

Yes. After switching it to b/a i got theta(ref)=-1

Answer 8

find out whats tan^1(-1)

Answer 9

tan^1(-1) or tan^-1(1)?
tan^1(-1) is -1.55 or -tan(1)

http://www.wolframalpha.com/input/?i=tan%5E1%28-1%29

Answer 10

\[\tan^{-1} (-1)\]

Answer 11

Okay, yeah tan^-1(-1) is -pi/4 or -45 degrees

Answer 12

now put that in 360 degrees form

Answer 13

find the angle that is coterminal to -45 degrees? Thats 315, right?

Answer 14

yea

Answer 15

you know how to make the polar form from there right?

Answer 16

oh wait its trigo form

Answer 17

Yea. I was stuck at theta(ref)= -1. I dont know what to do next

Answer 18

ok great you have the angles now you can form whatever it is

Answer 19

you should get \(\theta\) instantly from your eyeballs