Answer:

Step-by-step explanation:
Recall that 
<u>Part A:</u>
We are just squaring a binomial, so the FOIL method works great. Also, recall that
.

<u>Part B:</u>
The magnitude, or modulus, of some complex number
is given by
.
In
, assign values:

<u>Part C:</u>
In Part A, notice that when we square a complex number in the form
, our answer is still a complex number in the form
We have:

Expanding, we get:

This is still in the exact same form as
where:
corresponds with
corresponds with
Thus, we have the following system of equations:

Divide the second equation by
to isolate
:

Substitute this into the first equation:

This is a quadratic disguise, let
and solve like a normal quadratic.
Solving yields:

We stipulate
and therefore
is extraneous.
Thus, we have the following cases:

Notice that
. However, since
, two solutions will be extraneous and we will have only two roots.
Solving, we have:

Given the conditions
, the solutions to this system of equations are:

Therefore, the square roots of
are:

<u>Part D:</u>
The polar form of some complex number
is given by
, where
is the modulus of the complex number (as we found in Part B), and
(derive from right triangle in a complex plane).
We already found the value of the modulus/magnitude in Part B to be
.
The angular polar coordinate
is given by
and thus is:

Therefore, the polar form of
is:
