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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

Popular Examples

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factor (x+y+z)^3-x^3-y^3-z^3 factor

(x + y + z)^{3} - x^{3} - y^{3} - z^{3}

Frequently Asked Questions (FAQ)

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