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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 \cdot 1^{2} i + 3 \cdot 1 \cdot i^{2} + i^{3}

= 1^{3} + 3 \cdot 1^{2} i + 3 \cdot 1 \cdot i^{2} + i^{3}

Simplify

1^{3} + 3 \cdot 1^{2} i + 3 \cdot 1 \cdot 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