How to find the polar form of the complex number if given the rectangular form 7 - 5j?

The rectangular form of a complex number
is:

z = x + i*y, where x represents the real part and y the
imaginary part.

The polar form of a complex number is
written in terms of a distance from origin of coordinate system and an angle measured
from the positive x axis.

`z = r(cos theta + i*sin
theta)`

The length of the vector r can be found using the
real and imaginary parts of the complex number, which are given in rectangular
form.

We'll use Pythagorean theorem to determine the length
of the vector r, which is the hypotenuse of the right angle triangle, whose legs are the
real and imaginary parts.

`r^2 = x^2 +
y^2`

`r = sqrt(x^2 + y^2)`

In
this case, we'll identify x and y:

x = 7 and y =
-5.

`r = sqrt(7^2 +
(-5)^2)`

`r =
sqrt(74)`

`` Now, we'll find the angle `theta`  made by r
to positive x axis.

`tan theta =
y/x`

`tan theta = -5/7`

`theta
= arctan (-5/7)`

`theta = 324.48
degrees`

Therefore, the polar form of the
given complex number is:

`z =
(sqrt(74))(cos 324.48 + isin324.48).`