Find All Complex Number Solutions

${(z + 6)}^{2} = 2 i + 4$

Step 1

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

$z + 6 = \pm \sqrt{4 + 2 i}$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$z + 6 = \sqrt{4 + 2 i}$

Step 2.2

Subtract $6$ from both sides of the equation.

$z = \sqrt{4 + 2 i} - 6$

Step 2.3

Next, use the negative value of the $\pm$ to find the second solution.

$z + 6 = - \sqrt{4 + 2 i}$

Step 2.4

Subtract $6$ from both sides of the equation.

$z = - \sqrt{4 + 2 i} - 6$

Step 2.5

The complete solution is the result of both the positive and negative portions of the solution.

$z = \sqrt{4 + 2 i} - 6, - \sqrt{4 + 2 i} - 6$

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Complex Numbers and Vector Analysis

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Complex Numbers and Vector Analysis