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Linear Algebra Examples

2 + 3 i

$2 + 3 i$

Step 1

Use the formula

| a + b i | = \sqrt{a^{2} + b^{2}}

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

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

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

Step 2

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{4 + 3^{2}}

$\sqrt{4 + 3^{2}}$

Step 3

Raise

3

$3$ to the power of

2

$2$ .

\sqrt{4 + 9}

$\sqrt{4 + 9}$

Step 4

Add

4

$4$ and

9

$9$ .

\sqrt{13}

$\sqrt{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\sqrt{13}

$\sqrt{13}$

Decimal Form:

3.60555127 \dots

$3.60555127 \dots$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$