Help on math problem: Change the following complex numbers to polar form,?

Question

Change the following complex numbers to polar form:
z1 = -1 + i
z2 = -1 - i(square root of 3)
z3 = 5

Please help and possibly show steps
Thank you

Answer 1

1. r=sqrt(2) and angle=135 degrees
2. r=2 and angle= arctan(sqrt(3))--remember that this will be in the fourth quadrant.
3. r=5

Answer 2

Complex numbers are written in the form a + bi where a and b are real numbers and i has the standard definition.
These can be plotted in a rectangular coordinate axis where the horizontal axis is the real axis and the vertical axis is the imaginary axis.
So, the complex number a + bi can be plotted in the complex plane at the point represented by the ordered pair (a, b).

Polar coordinates are in the form (r, theta) where r is the distance from the origin and theta is the angle from the polar axis, otherwise known as the positive x-axis or the positive real axis.
We can use trigonometric and geometric properties to find the coordinates r and theta.
r^2 = a^2 + b^2 and
tan(theta) = (b/a)

So, z1 = -1 + 1
r^2 = (-1)^2 + (1)^2
r^2 = 1 + 1
r^2 = 2
r = sqrt(2)
tan(theta) = (1/-1)
tan(theta) = -1
theta = -(pi)/4
We need to adjust theta to coordinate with the quadrant of the complex number.
z1 = -1 + i is in the third quadrant of the complex plane, so
theta = 3(pi)/4.

Therefore z1 can be represented by the polar coordinates
(sqrt(2), 3(pi)/4)

The other two can be found in the same way.

Answer 3

z1= 2^(.5) * e^(-45 degree)
z2=2^(1/6)* e^(45 degree)
z3=5

if you find it difficult to understand what i just wrote contact me on my email because without math symbols were not available and i could not write it more clear