Question

Write z = 1-i in trigonometric(polar)form, where the argument "theta" satisfies 0<= "theta" < 2 pie

Answer 1

For z= x-iy

\[r=\sqrt{x ^{2}+y ^{2}}\]\[r=\sqrt{1^{2}+(-1)^{2}}\]\[r=\sqrt{2}\]\[\tan \theta= (-1/1)\]\[\theta=-45\]or\[\theta=360-45\]\[\theta=315\]\[\sqrt{2}(\cos315+\sin315)\]

Answer 2

thanks, how do I know when to use sin, cos or tan to get to the answer?

Answer 3

1. I would plot the point first in the complex plane and note the quadrant.

2. Then I would draw a line segment, from the orgin to the point..

3. From there you can always find theta by noting the right triangle formed by the x-axis, y-axis and the point.

Answer 4

Thanks for all your help