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Popular >

simplify (2-2i)^3

Solution

simplify

(2 - 2 i)^{3}

Solution

- 16 - 16 i

Solution steps

(2 - 2 i)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

2^{3} - 3 \cdot 2^{2} \cdot 2 i + 3 \cdot 2 (2 i)^{2} - (2 i)^{3} : - 16 i - 16

= - 16 i - 16

Rewrite in standard complex form:

- 16 - 16 i

= - 16 - 16 i

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Frequently Asked Questions (FAQ)

What is (2-2i)^3 ?
The solution to (2-2i)^3 is -16-16i