化简 (3y+4i)^2

解答

化简

(3 y + 4 i)^{2}

(9 y^{2} - 16) + 24 y i

求解步骤

(3 y + 4 i)^{2}

使用完全平方公式:

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

(3 y + 4 i)^{2} = (3 y)^{2} + 2 \cdot 3 y \cdot 4 i + (4 i)^{2}

= (3 y)^{2} + 2 \cdot 3 y \cdot 4 i + (4 i)^{2}

(3 y)^{2} = 9 y^{2}

2 \cdot 3 y \cdot 4 i = 24 y i

(4 i)^{2} = - 16

= 9 y^{2} + 24 y i - 16

Rewrite in standard complex form:

(9 y^{2} - 16) + 24 y i

= (9 y^{2} - 16) + 24 y i

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