What are the steps to simplify the expression (4+6i)(4−6i) ?

Answer 1

Recognize this equation as the difference of two squares format. (x+y)(x-y) = x^2-y^2.

Thus (4 + 6i)(4-6i) = 16 - 36i^2

Since i^2 = -1 then -36 i^2 = + 36.

Then add: 16 + 36 = 52; 52 is the answer.

Answer 2

You will want to multiply these binomials using what is referred to as FOIL (First, Inner, Outer, Last)

This is where you multiple the first factor in each binomial, the factors appearing to be towards the center, the external factors, and the last factor in each binomial. This is similar to the distributive process, but for two binomials rather than one factor and a binomial.

(4+6i)(4-6i)

First: 4*4 = 16

Outer: 4*-(6i) = -24i

Inner: 6i*4 = 24i

Last: 6i*(-6i) = (-36i)^2

Now we combine all the factors into a horizontal viewing:

16 - 24i + 24i - 36i^2

Combine like terms (numbers, letters, etc.)

16 - 36i^2

In order of least to greatest exponents this would be written as (-36i)^2 + 16

If your equation equalled/equals 0, you can go further and solve for i, but it looks like all that is being asked is to simplify.