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Popular >

simplify (1+2i)^3

Solution

simplify

(1 + 2 i)^{3}

Solution

- 11 - 2 i

Solution steps

(1 + 2 i)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

1^{3} + 3 \cdot 1^{2} \cdot 2 i + 3 \cdot 1 \cdot (2 i)^{2} + (2 i)^{3} : - 2 i - 11

= - 2 i - 11

Rewrite in standard complex form:

- 11 - 2 i

= - 11 - 2 i

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Frequently Asked Questions (FAQ)

What is (1+2i)^3 ?
The solution to (1+2i)^3 is -11-2i