Precalculus Examples

$f (x) = (x - 5 i) (x + 5 i)$

Step 1

Set $(x - 5 i) (x + 5 i)$ equal to $0$ .

$(x - 5 i) (x + 5 i) = 0$

Step 2

Solve for $x$ .

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Step 2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 5 i = 0$

$x + 5 i = 0$

Step 2.2

Set $x - 5 i$ equal to $0$ and solve for $x$ .

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Step 2.2.1

Set $x - 5 i$ equal to $0$ .

$x - 5 i = 0$

Step 2.2.2

Add $5 i$ to both sides of the equation.

$x = 5 i$

Step 2.3

Set $x + 5 i$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x + 5 i$ equal to $0$ .

$x + 5 i = 0$

Step 2.3.2

Subtract $5 i$ from both sides of the equation.

$x = - 5 i$

Step 2.4

The final solution is all the values that make $(x - 5 i) (x + 5 i) = 0$ true.

$x = 5 i, - 5 i$

Step 3