Calculus Examples

$z^{3} - 4 \sqrt{3} - 4 i = 0$

Step 1

Move all terms not containing $z$ to the right side of the equation.

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Step 1.1

Add $4 \sqrt{3}$ to both sides of the equation.

$z^{3} - 4 i = 4 \sqrt{3}$

Step 1.2

Add $4 i$ to both sides of the equation.

$z^{3} = 4 \sqrt{3} + 4 i$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$z = \sqrt[3]{4 \sqrt{3} + 4 i}$

Step 3

Factor $4$ out of $4 \sqrt{3} + 4 i$ .

$z = \sqrt[3]{4 (\sqrt{3} + i)}$