Basic Math Examples

$| - 2 + 3 i | + | - 2 + 3 i + 3 - 2 i |$

Step 1

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

$\sqrt{{(- 2)}^{2} + 3^{2}} + | - 2 + 3 i + 3 - 2 i |$

Step 2

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

$\sqrt{4 + 3^{2}} + | - 2 + 3 i + 3 - 2 i |$

Step 3

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

$\sqrt{4 + 9} + | - 2 + 3 i + 3 - 2 i |$

Step 4

Add $4$ and $9$ .

$\sqrt{13} + | - 2 + 3 i + 3 - 2 i |$

Step 5

Add $- 2$ and $3$ .

$\sqrt{13} + | 1 + 3 i - 2 i |$

Step 6

Subtract $2 i$ from $3 i$ .

$\sqrt{13} + | 1 + i |$

Step 7

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

$\sqrt{13} + \sqrt{1^{2} + 1^{2}}$

Step 8

One to any power is one.

$\sqrt{13} + \sqrt{1 + 1^{2}}$

Step 9

One to any power is one.

$\sqrt{13} + \sqrt{1 + 1}$

Step 10

Add $1$ and $1$ .

$\sqrt{13} + \sqrt{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\sqrt{13} + \sqrt{2}$

Decimal Form:

$5.01976483 \dots$