Simplify (4+3i)^2.

To simplify the complex number raised to square, we'll expand
the square, using the formula:

(a+b)^2 = a^2 + 2ab +
b^2

We'll put a = 4 and b =
3i:

(4+3i)^2 = 4^2 + 2*4*3i +
(3i)^2

(4+3i)^2 = 16 + 24i + 9i^2

But
i^2 = -1

(4+3i)^2 = 16 + 24i - 9

We'll
combine the real parts:

(4+3i)^2 = 7 +
24i

The simplified form of the complex number raised
to square is:

(z)^2 = 7 + 24i, where z
= 4+3i.