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Popular >

expand (1-i)^3

Solution

expand

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