Question

Write z = -5 + 5i in trigonometric form.

Answer 1

D?

Answer 2

Hint:Sketch the point it on the complex plane

Answer 3

I found -(pi)/(4)

Answer 4

before

Answer 5

??

Answer 6

What does that graph mean?

Answer 7

-5 + 5i is in the form a+bi

a = -5
b = 5

you can plot a+bi on the complex number plane as the ordered pair (a,b)

which is why satellite73 plotted the point (-5,5)

Answer 8

it means the angle is easy to find
if you use arctangent here it will not work because you are in the wrong quadrant

Answer 9

http://img.sparknotes.com/figures/A/a28868a2f5deab01f6e8c7727c2ee7a4/complexplane.gif

Answer 10

if you took \(\tan^{-1}(-1)\) you get \(-\frac{\pi}{4}\) but you are not in quadrant 4, you are in quadrant 2

Answer 11

So it's 3pi/4 instead, right?

Answer 12

yes

Answer 13

you cannot use arctan unless you are in quadrant 1 or 4

Answer 14

well you can use arctan, just add on pi to get to the right quadrant

Answer 15

?

Answer 16

you have to either know it, or use
\[\cos(\theta)=\frac{a}{r}\] and \[\sin(\theta)=\frac{b}{r}\]

Answer 17

as satellite73 said, arctan(-1) = -pi/4

add on pi to get to 3pi/4

(-pi/4) + (pi) = (-pi/4) + (4pi/4) = (-pi+4pi)/4 = 3pi/4

Answer 18

or what @jim_thompson5910 said, but in any case you have to know what quadrant you are in before you start