simplify (x-2i)^2

Solution

simplify

(x - 2 i)^{2}

(x^{2} - 4) - 4 x i

Solution steps

(x - 2 i)^{2}

Apply Perfect Square Formula:

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

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

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

- 2 x \cdot 2 i = - 4 x i

(2 i)^{2} = - 4

= x^{2} - 4 x i - 4

Rewrite in standard complex form:

(x^{2} - 4) - 4 x i

= (x^{2} - 4) - 4 x i

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