化简 (1-2zi)^2

解答

化简

(1 - 2 z i)^{2}

(1 - 4 z^{2}) - 4 z i

求解步骤

(1 - 2 z i)^{2}

使用完全平方公式:

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

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

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

1^{2} = 1

- 2 \cdot 1 \cdot 2 z i = - 4 z i

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

= 1 - 4 z i - 4 z^{2}

Rewrite in standard complex form:

(1 - 4 z^{2}) - 4 z i

= (1 - 4 z^{2}) - 4 z i

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