Multiplying Complex Numbers

Question

1. Find the solutions to .
2. Write  as either an integer or an integer multiple of .

Answer 1

x² = -20

√(x²) = √(-20)

x = +/- √(-1*20)

x = +/- √(-1) * √-20

Since the √(-1) = i, we now have +/- i * √(20)

We can further simplify the square root of 20:

√(20) = √(4*5) = √(4) * √(5) = 2 * √5

Therefore, there are two solutions to number 1:

2i√(5)

-2i√(5)

-(7i)²

We can apply the square to each term being multiplied:

-(7² * i²)

-(49 * i²)

Since i = √(-1), i² = -1

-(49 * (-1))

-(-49)

49

Answer 2

1. x=sqr(-20) = isqr(20) = +2isqr5 = about +4.4i
2. -(7i)^2 = -49i^2 = -49(-1) = 49