What is (-4+(6i)/n)^2 ?

The solution to (-4+(6i)/n)^2 is (16n^2-36}{n^2}-\frac{48)/n i

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simplify (-4+(6i)/n)^2

simplify

(- 4 + \frac{6 i}{n})^{2}

\frac{16 n ^{2} - 36}{n ^{2}} - \frac{48}{n} i

Solution steps

(- 4 + \frac{6 i}{n})^{2}

Apply Perfect Square Formula:

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

(- 4 + \frac{6 i}{n})^{2} = (- 4)^{2} + 2 (- 4) \frac{6 i}{n} + (\frac{6 i}{n})^{2}

= (- 4)^{2} + 2 (- 4) \frac{6 i}{n} + (\frac{6 i}{n})^{2}

(- 4)^{2} = 16

2 (- 4) \frac{6 i}{n} = - 8 \cdot \frac{6 i}{n}

(\frac{6 i}{n})^{2} = - \frac{36}{n ^{2}}

= 16 - 8 \cdot \frac{6 i}{n} - \frac{36}{n ^{2}}

Simplify

16 - 8 \cdot \frac{6 i}{n} - \frac{36}{n ^{2}} : \frac{16 n ^{2} - 36}{n ^{2}} - \frac{48}{n} i

= \frac{16 n ^{2} - 36}{n ^{2}} - \frac{48}{n} i

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What is (-4+(6i)/n)^2 ?
The solution to (-4+(6i)/n)^2 is (16n^2-36}{n^2}-\frac{48)/n i