What is (3/5+(sqrt(5))/2 i)^2 ?

The solution to (3/5+(sqrt(5))/2 i)^2 is -89/100+3/(sqrt(5))i

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simplify (3/5+(sqrt(5))/2 i)^2

simplify

(\frac{3}{5} + \frac{5}{2} i)^{2}

- \frac{89}{100} + \frac{3}{5} i

Solution steps

(\frac{3}{5} + \frac{5}{2} i)^{2}

Apply Perfect Square Formula:

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

(\frac{3}{5} + \frac{5}{2} i)^{2} = (\frac{3}{5})^{2} + 2 \cdot \frac{3}{5} \cdot \frac{5}{2} i + (\frac{5}{2} i)^{2}

= (\frac{3}{5})^{2} + 2 \cdot \frac{3}{5} \cdot \frac{5}{2} i + (\frac{5}{2} i)^{2}

Simplify

(\frac{3}{5})^{2} + 2 \cdot \frac{3}{5} \cdot \frac{5}{2} i + (\frac{5}{2} i)^{2} : - \frac{89}{100} + \frac{3}{5} i

= - \frac{89}{100} + \frac{3}{5} i

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What is (3/5+(sqrt(5))/2 i)^2 ?
The solution to (3/5+(sqrt(5))/2 i)^2 is -89/100+3/(sqrt(5))i