Basic Math Examples

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

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

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}} + | - 2 + 3 i + 3 - 2 i |

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

Step 2

Raise

- 2

$- 2$ to the power of

2

$2$ .

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

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

Step 3

Raise

3

$3$ to the power of

2

$2$ .

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

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

Step 4

Add

4

$4$ and

9

$9$ .

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

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

Step 5

Add

- 2

$- 2$ and

3

$3$ .

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

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

Step 6

Subtract

2 i

$2 i$ from

3 i

$3 i$ .

\sqrt{13} + | 1 + i |

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

Step 7

Use the formula

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

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

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

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

Step 8

One to any power is one.

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

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

Step 9

One to any power is one.

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

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

Step 10

Add

1

$1$ and

1

$1$ .

\sqrt{13} + \sqrt{2}

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

Step 11

The result can be shown in multiple forms.

Exact Form:

\sqrt{13} + \sqrt{2}

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

Decimal Form:

5.01976483 \dots

$5.01976483 \dots$

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

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

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