Question

Express the complex number in trigonometric form.

2 - 2i

Answer 1

so, you don't have the formulas for converting complex to trigs?

Answer 2

@jdoe0001 no

Answer 3

ok

Answer 4

@jdoe0001 can you help?

Answer 5

\[a+bi = r(cos(\theta)+i\ sin(\theta))\]
now how to find out what "r" is?

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

now, how to find out what the angle/theta is?
\[tan(\theta)=\frac{b}{a}\]

Answer 6

what signs "a" and "b" have will tell you what quadrant they're in, and thus you use THAT angle with THAT
tangent

Answer 7

in this particular case, 2-2i, a=(2), b=(-2), so b[y coordinate] is negative, and a[x coordinate] is positive, that means, where X is positive and Y is negative :), that quadrant, that angle with that tangent

Answer 8

@jdoe0001 that's all the quadrants

Answer 9

mmm, no all quadrants have such neg/pos combination, the signs actually alternate some from quadrant to quadrant

Answer 10

take a peek at your Unitary Circle, if you have any

Answer 11

@jdoe0001 quadrant 3 has it

Answer 12

so, that's your quadrant :)

Answer 13

@jdoe0001 what now

Answer 14

well, you need to find "r" and the tangent :), using the formulas

Answer 15

once found, just combine them in the \[r(cos(\theta)+i\ \ sin(\theta))\] form, and that's the converted version

Answer 16

confused still?

Answer 17

@jdoe001 no I got it ... 2√(2)(cos((5π)/(4))+isin((5π)/(4))) ?

Answer 18

well, looks actually fine, more or less, but tan(5pi/4) = 1, no -1, your tangent is -2/2 = -1

Answer 19

and also 5pi/4 is on the 3rd quadrant

Answer 20

ohh, I did say it was so... well, my bad :|, is not the 3rd anyway :)

Answer 21

bear in mind that \[tan(\theta)=\frac{-2}{2}=-1\]

Answer 22

@jdoe0001 now what

Answer 23

check your unit circle, see where Y is negative and X is positive, is not the 3rd quadrant though

Answer 24

thus is not 5pi/4, the "r" is fine though

Answer 25

@jdoe0001 quadrant 4

Answer 26

:)

Answer 27

@jdoe0001 7pi/4

Answer 28

yep, that's what I got