Question

Simplify xi(I-7i) ^2

Answer 1

Note what i actually represents.
i is the very basis of a whole new level of counting. When finding discriminants, we often say that a quadratic has no real roots if the discriminant is 0. Needless to say, there are roots, they are just imaginary.

$\sqrt{-1}$, in real terms, is non-existent. That is, there are no numbers in the real number system that when multiplied by itself produces a result of -1. This is what i unit represents.

Let's tackle this problem in smaller steps.
Let's first expand our brackets.

(i - 7i)² = (-6i)² = 36i²
Now, let's distribute the xi.

xi(i - 7i)² = xi(36i²) = 36xi³ = $-36x\sqrt{-1}$ = -36xi

Answer 2

FOIL out inside the parenthesis to get a number, -36. Then multiply that by xi to get -36xi