Question

Is the square of a complex number always a real number? Explain how, please I would like to finish this tonight.

Answer 1

The absolute square of a complex number is calculated by multiplying it by its complex conjugate. This give the magnitude squared of the complex number. The absolute square is Always Real. We will use complex exponentials all the time.

Answer 2

Explanation:

I don't thing it is very often unless it is of the form

5i

When you square that, you get a real number (5i)^2 = - 25

On the other hand when you have a binomial like

3 + 2i

and you square that, the result is still a complex number.

(3+2i)(3+2i) = 9 + 6i + 6i + 4i^2 = 5 + 12i