What is (sqrt(2)-4i)^2 ?

The solution to (sqrt(2)-4i)^2 is -14-8sqrt(2)i

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simplify (sqrt(2)-4i)^2

simplify

(2 - 4 i)^{2}

- 14 - 82 i

Solution steps

(2 - 4 i)^{2}

Apply Perfect Square Formula:

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

(2 - 4 i)^{2} = (2)^{2} - 22 \cdot 4 i + (4 i)^{2}

= (2)^{2} - 22 \cdot 4 i + (4 i)^{2}

Simplify

(2)^{2} - 22 \cdot 4 i + (4 i)^{2} : - 82 i - 14

= - 82 i - 14

Rewrite in standard complex form:

- 14 - 82 i

= - 14 - 82 i

x^{a} + x^{a + b}

351

\frac{5}{2} - \frac{x}{3}

5 x^{2} (x + 2 y) (x^{2} - 2 x y + 4 y^{2})

3 \frac{2}{3} - 2 \frac{3}{2}