Algebra Examples

$| 7 - i |$

Step 1

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

$\sqrt{7^{2} + {(- 1)}^{2}}$

Step 2

Raise $7$ to the power of $2$ .

$\sqrt{49 + {(- 1)}^{2}}$

Step 3

Raise $- 1$ to the power of $2$ .

$\sqrt{49 + 1}$

Step 4

Add $49$ and $1$ .

$\sqrt{50}$

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:

$7.07106781 \dots$