Simplify (4+- square root of -16)/4

$\frac{4 + - \sqrt{- 16}}{4}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$\frac{4 - \sqrt{- 16}}{4}$

Step 2

Pull out imaginary unit $i$ .

Rewrite $- 16$ as $- 1 (16)$ .

$\frac{4 - \sqrt{- 1 (16)}}{4}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$\frac{4 - (\sqrt{- 1} \cdot \sqrt{16})}{4}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{4 - (i \cdot \sqrt{16})}{4}$

Step 3

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$\frac{4 - i \cdot \sqrt{4^{2}}}{4}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4 - i \cdot 4}{4}$

Multiply $4$ by $- 1$ .

$\frac{4 - 4 i}{4}$

Step 4

Cancel the common factor of $4 - 4 i$ and $4$ .

Factor $4$ out of $4$ .

$\frac{4 \cdot 1 - 4 i}{4}$

Factor $4$ out of $- 4 i$ .

$\frac{4 \cdot 1 + 4 (- i)}{4}$

Factor $4$ out of $4 (1) + 4 (- i)$ .

$\frac{4 (1 - i)}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (1 - i)}{4 (1)}$

Cancel the common factor.

$\frac{4 (1 - i)}{4 \cdot 1}$

Rewrite the expression.

$\frac{1 - i}{1}$

Divide $1 - i$ by $1$ .

$1 - i$

Simplify (4+- square root of -16)/4

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