Basic Math Examples

$\frac{| 1 + 2 i |}{| 2 - i |}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\sqrt{1^{2} + 2^{2}}}{| 2 - i |}$

Step 1.2

One to any power is one.

$\frac{\sqrt{1 + 2^{2}}}{| 2 - i |}$

Step 1.3

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

$\frac{\sqrt{1 + 4}}{| 2 - i |}$

Step 1.4

Add $1$ and $4$ .

$\frac{\sqrt{5}}{| 2 - i |}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\sqrt{5}}{\sqrt{2^{2} + {(- 1)}^{2}}}$

Step 2.2

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

$\frac{\sqrt{5}}{\sqrt{4 + {(- 1)}^{2}}}$

Step 2.3

Raise $- 1$ to the power of $2$ .

$\frac{\sqrt{5}}{\sqrt{4 + 1}}$

Step 2.4

Add $4$ and $1$ .

$\frac{\sqrt{5}}{\sqrt{5}}$

Step 3

Cancel the common factor of $\sqrt{5}$ .

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Step 3.1

Cancel the common factor.

$\frac{\sqrt{5}}{\sqrt{5}}$

Step 3.2

Rewrite the expression.

$1$