化简 (3+3i)^3

解答

化简

(3 + 3 i)^{3}

- 54 + 54 i

求解步骤

(3 + 3 i)^{3}

使用完全立方公式:

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

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

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

化简

3^{3} + 3 \cdot 3^{2} \cdot 3 i + 3 \cdot 3 (3 i)^{2} + (3 i)^{3} : 54 i - 54

= 54 i - 54

Rewrite in standard complex form:

- 54 + 54 i

= - 54 + 54 i

s im pl i f y 175 + 63

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s im pl i f y lo g_{\frac{1}{3}} (1)

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