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Popular >

simplify (-1+sqrt(3)i)^3

Solution

simplify

(- 1 + 3 i)^{3}

Solution

8

Solution steps

(- 1 + 3 i)^{3}

Apply Perfect Cube Formula:

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

(- 1 + 3 i)^{3} = (- 1)^{3} + 3 (- 1)^{2} 3 i + 3 (- 1) (3 i)^{2} + (3 i)^{3}

= (- 1)^{3} + 3 (- 1)^{2} 3 i + 3 (- 1) (3 i)^{2} + (3 i)^{3}

Simplify

(- 1)^{3} + 3 (- 1)^{2} 3 i + 3 (- 1) (3 i)^{2} + (3 i)^{3} : 8

= 8

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Frequently Asked Questions (FAQ)

What is (-1+sqrt(3)i)^3 ?
The solution to (-1+sqrt(3)i)^3 is 8