What is (1/2-1/(sqrt(2))i)^2 ?

The solution to (1/2-1/(sqrt(2))i)^2 is -1/4-1/(sqrt(2))i

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simplify (1/2-1/(sqrt(2))i)^2

simplify

(\frac{1}{2} - \frac{1}{2} i)^{2}

- \frac{1}{4} - \frac{1}{2} i

Solution steps

(\frac{1}{2} - \frac{1}{2} i)^{2}

Apply Perfect Square Formula:

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

(\frac{1}{2} - \frac{1}{2} i)^{2} = (\frac{1}{2})^{2} - 2 \cdot \frac{1}{2} \cdot \frac{1}{2} i + (\frac{1}{2} i)^{2}

= (\frac{1}{2})^{2} - 2 \cdot \frac{1}{2} \cdot \frac{1}{2} i + (\frac{1}{2} i)^{2}

Simplify

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

= - \frac{1}{4} - \frac{1}{2} i

5 (x - 1)^{2} - 5 x^{2}

15 x^{2} - 2 x - 8

3 b + b

x^{2} - 14 x + 40

\frac{5}{6} = \frac{x - 4}{12}

What is (1/2-1/(sqrt(2))i)^2 ?
The solution to (1/2-1/(sqrt(2))i)^2 is -1/4-1/(sqrt(2))i