Trigonometry Examples

$| a c + c i |$

Step 1

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

$\sqrt{{(a c)}^{2} + c^{2}}$

Step 2

Apply the product rule to $a c$ .

$\sqrt{a^{2} c^{2} + c^{2}}$

Step 3

Factor $c^{2}$ out of $a^{2} c^{2} + c^{2}$ .

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Step 3.1

Factor $c^{2}$ out of $a^{2} c^{2}$ .

$\sqrt{c^{2} a^{2} + c^{2}}$

Step 3.2

Multiply by $1$ .

$\sqrt{c^{2} a^{2} + c^{2} \cdot 1}$

Step 3.3

Factor $c^{2}$ out of $c^{2} a^{2} + c^{2} \cdot 1$ .

$\sqrt{c^{2} (a^{2} + 1)}$

Step 4

Rewrite $1$ as $1^{2}$ .

$\sqrt{c^{2} (a^{2} + 1^{2})}$

Step 5

Pull terms out from under the radical.

$c \sqrt{a^{2} + 1^{2}}$

Step 6

One to any power is one.

$c \sqrt{a^{2} + 1}$