化简 (5x^2+4yi)^2

解答

化简

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

(25 x^{4} - 16 y^{2}) + 40 x^{2} y i

求解步骤

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

使用完全平方公式:

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

(5 x^{2} + 4 y i)^{2} = (5 x^{2})^{2} + 2 \cdot 5 x^{2} \cdot 4 y i + (4 y i)^{2}

= (5 x^{2})^{2} + 2 \cdot 5 x^{2} \cdot 4 y i + (4 y i)^{2}

(5 x^{2})^{2} = 25 x^{4}

2 \cdot 5 x^{2} \cdot 4 y i = 40 x^{2} y i

(4 y i)^{2} = - 16 y^{2}

= 25 x^{4} + 40 x^{2} y i - 16 y^{2}

Rewrite in standard complex form:

(25 x^{4} - 16 y^{2}) + 40 x^{2} y i

= (25 x^{4} - 16 y^{2}) + 40 x^{2} y i

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s im pl i f y (2 + z i)^{2}

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