Find the Magnitude |5+4i|

$| 5 + 4 i |$

Step 1

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

$\sqrt{5^{2} + 4^{2}}$

Step 2

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

$\sqrt{25 + 4^{2}}$

Step 3

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

$\sqrt{25 + 16}$

Step 4

Add $25$ and $16$ .

$\sqrt{41}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{41}$

Decimal Form:

$6.40312423 \dots$