Basic Math Examples

$| - 5 - 5 i |$

Step 1

Use the formula $| a + b i | = \sqrt{a^{2} + b^{2}}$ to find the magnitude.

$\sqrt{{(- 5)}^{2} + {(- 5)}^{2}}$

Step 2

Raise $- 5$ to the power of $2$ .

$\sqrt{25 + {(- 5)}^{2}}$

Step 3

Raise $- 5$ to the power of $2$ .

$\sqrt{25 + 25}$

Step 4

Add $25$ and $25$ .

$\sqrt{50}$

Step 5

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 5.1

Factor $25$ out of $50$ .

$\sqrt{25 (2)}$

Step 5.2

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$5 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{2}$

Decimal Form:

$7.07106781 \dots$