Simplify |4-6i|

$| 4 - 6 i |$

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

$\sqrt{4^{2} + {(- 6)}^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{16 + {(- 6)}^{2}}$

Raise $- 6$ to the power of $2$ .

$\sqrt{16 + 36}$

Add $16$ and $36$ .

$\sqrt{52}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$\sqrt{4 (13)}$

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

$\sqrt{2^{2} \cdot 13}$

Pull terms out from under the radical.

$2 \sqrt{13}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{13}$

Decimal Form:

$7.21110255 \dots$