What is 3(1+(4i)/n)^2 ?

The solution to 3(1+(4i)/n)^2 is (3n^2-48}{n^2}+\frac{24)/n i

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simplify 3(1+(4i)/n)^2

simplify

3 (1 + \frac{4 i}{n})^{2}

\frac{3 n ^{2} - 48}{n ^{2}} + \frac{24}{n} i

Solution steps

3 (1 + \frac{4 i}{n})^{2}

Expand

(1 + \frac{4 i}{n})^{2} : 1 + 2 \cdot \frac{4 i}{n} - \frac{16}{n ^{2}}

= 3 (1 + 2 \cdot \frac{4 i}{n} - \frac{16}{n ^{2}})

Apply the distributive law:

m (a + b + c) = ma + mb + m c

3 (1 + 2 \cdot \frac{4 i}{n} - \frac{16}{n ^{2}}) = 3 \cdot 1 + 3 \cdot 2 \cdot \frac{4 i}{n} + 3 (- \frac{16}{n ^{2}})

= 3 \cdot 1 + 3 \cdot 2 \cdot \frac{4 i}{n} + 3 (- \frac{16}{n ^{2}})

Simplify

3 \cdot 1 + 3 \cdot 2 \cdot \frac{4 i}{n} + 3 (- \frac{16}{n ^{2}}) : \frac{3 n ^{2} - 48}{n ^{2}} + \frac{24}{n} i

= \frac{3 n ^{2} - 48}{n ^{2}} + \frac{24}{n} i

(9 + 2) (4 + 7)

sin (a) \cdot (1 + tan (a)) + cos (a) \cdot (1 + cot (a))

(1 - cos (4 x))^{4}

(1 - cos (4 x))^{2}

(cos (θ) + i sin (θ))^{3}

What is 3(1+(4i)/n)^2 ?
The solution to 3(1+(4i)/n)^2 is (3n^2-48}{n^2}+\frac{24)/n i