Question

check please
True or false: As long as its argument is restricted to [0,2pi] the polar form of a complex number is unique.

Answer 1

i think it's false but i want to make sure that im right

Answer 2

why do you think it's false?

Answer 3

because the argument is not unique for complex numbers

Answer 4

here is an xy axis

Answer 5

let's say we plotted the point (x,y) = (0,1)

Answer 6

what is the polar form of that number?

Answer 7

of that point I mean

Answer 8

is it (cos(pi/2) + sin(pi/2)) ?

Answer 9

what is r? what is theta?

Answer 10

r is 0 and theta is pi/2?

Answer 11

r is 1 actually

Answer 12

you start at the origin, or the pole, and you go 1 unit away from it to land on (0,1)

Answer 13

the angle is pi/2, or 90 degrees

Answer 14

oh okay

Answer 15

but this isn't the only way to represent the point (0,1)

we could have (r,theta) = (-1, 270 degrees)

so you rotate 270 degrees