Algebra Examples

$| 3 + 9 i |$

Step 1

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

$\sqrt{3^{2} + 9^{2}}$

Step 2

Raise $3$ to the power of $2$ .

$\sqrt{9 + 9^{2}}$

Step 3

Raise $9$ to the power of $2$ .

$\sqrt{9 + 81}$

Step 4

Add $9$ and $81$ .

$\sqrt{90}$

Step 5

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 5.1

Factor $9$ out of $90$ .

$\sqrt{9 (10)}$

Step 5.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 10}$

Step 6

Pull terms out from under the radical.

$3 \sqrt{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{10}$

Decimal Form:

$9.48683298 \dots$