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Popular >

simplify (3+4i)^3

Solution

simplify

(3 + 4 i)^{3}

Solution

- 117 + 44 i

Solution steps

(3 + 4 i)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

3^{3} + 3 \cdot 3^{2} \cdot 4 i + 3 \cdot 3 (4 i)^{2} + (4 i)^{3} : 44 i - 117

= 44 i - 117

Rewrite in standard complex form:

- 117 + 44 i

= - 117 + 44 i

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Frequently Asked Questions (FAQ)

What is (3+4i)^3 ?
The solution to (3+4i)^3 is -117+44i