How do you simplify (4+4i)/(2i)4+4i2i?

1 Answer
Sep 29, 2016

Multiply by the complex conjugate in both the numerator and denominator.

Explanation:

To simplify this expression, we need to remove the imaginary component in the denominator.

So, we multiply by the complex conjugate of 2i2i which is -2i2i on both the numerator and denominator

(4+4i)/(2i) * ((-2i)/(-2i))4+4i2i(2i2i)

((-2i)/(-2i))(2i2i) evaluates to 1, so multiplying by it does not change the value of our expression.

Multiplying through, we find (-8i-8i^2)/(-4i^2)8i8i24i2

We know i^2 = -1i2=1, so we replace in the expression and get:

(-8i+8)/48i+84

Since all terms have a 4, we can divide through by it, getting our answer:

-2i+22i+2