What is (-2+(3i)/n)^2 ?

The solution to (-2+(3i)/n)^2 is (4n^2-9}{n^2}-\frac{12)/n i

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simplify (-2+(3i)/n)^2

simplify

(- 2 + \frac{3 i}{n})^{2}

\frac{4 n ^{2} - 9}{n ^{2}} - \frac{12}{n} i

Solution steps

(- 2 + \frac{3 i}{n})^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(- 2 + \frac{3 i}{n})^{2} = (- 2)^{2} + 2 (- 2) \frac{3 i}{n} + (\frac{3 i}{n})^{2}

= (- 2)^{2} + 2 (- 2) \frac{3 i}{n} + (\frac{3 i}{n})^{2}

Simplify

(- 2)^{2} + 2 (- 2) \frac{3 i}{n} + (\frac{3 i}{n})^{2} : \frac{4 n ^{2} - 9}{n ^{2}} - \frac{12}{n} i

= \frac{4 n ^{2} - 9}{n ^{2}} - \frac{12}{n} i

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What is (-2+(3i)/n)^2 ?
The solution to (-2+(3i)/n)^2 is (4n^2-9}{n^2}-\frac{12)/n i