化简 (a-bi)^3

解答

化简

(a - bi)^{3}

(a^{3} - 3 a b^{2}) + (- 3 a^{2} b + b^{3}) i

求解步骤

(a - bi)^{3}

使用完全立方公式:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(a - bi)^{3} = a^{3} - 3 a^{2} bi + 3 a (bi)^{2} - (bi)^{3}

= a^{3} - 3 a^{2} bi + 3 a (bi)^{2} - (bi)^{3}

化简

a^{3} - 3 a^{2} bi + 3 a (bi)^{2} - (bi)^{3} : a^{3} - 3 a^{2} bi - 3 a b^{2} + b^{3} i

= a^{3} - 3 a^{2} bi - 3 a b^{2} + b^{3} i

Rewrite in standard complex form:

(a^{3} - 3 a b^{2}) + (- 3 a^{2} b + b^{3}) i

= (a^{3} - 3 a b^{2}) + (- 3 a^{2} b + b^{3}) i

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