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Popular >

simplify (-1+i)^3

Solution

simplify

(- 1 + i)^{3}

Solution

2 + 2 i

Solution steps

(- 1 + i)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

= 2 i + 2

Rewrite in standard complex form:

2 + 2 i

= 2 + 2 i

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Frequently Asked Questions (FAQ)

What is (-1+i)^3 ?
The solution to (-1+i)^3 is 2+2i