How do you simplify $\frac{4 + 4 i}{2 i}$ $(4+4i)/(2i)$ ?

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Answer 1 · 2016-09-29T14:49:34

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

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

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

$\frac{4 + 4 i}{2 i} \cdot (\frac{- 2 i}{- 2 i})$ $(4+4i)/(2i) * ((-2i)/(-2i))$

$(\frac{- 2 i}{- 2 i})$ $((-2i)/(-2i))$ evaluates to 1, so multiplying by it does not change the value of our expression.

Multiplying through, we find $\frac{- 8 i - 8 i^{2}}{- 4 i^{2}}$ $(-8i-8i^2)/(-4i^2)$

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

$\frac{- 8 i + 8}{4}$ $(-8i+8)/4$

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

$- 2 i + 2$ $-2i+2$

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