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Popular >

simplify (5-2i)^3

Solution

simplify

(5 - 2 i)^{3}

Solution

65 - 142 i

Solution steps

(5 - 2 i)^{3}

Apply Perfect Cube Formula:

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

(5 - 2 i)^{3} = 5^{3} - 3 \cdot 5^{2} \cdot 2 i + 3 \cdot 5 (2 i)^{2} - (2 i)^{3}

= 5^{3} - 3 \cdot 5^{2} \cdot 2 i + 3 \cdot 5 (2 i)^{2} - (2 i)^{3}

Simplify

5^{3} - 3 \cdot 5^{2} \cdot 2 i + 3 \cdot 5 (2 i)^{2} - (2 i)^{3} : - 142 i + 65

= - 142 i + 65

Rewrite in standard complex form:

65 - 142 i

= 65 - 142 i

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Frequently Asked Questions (FAQ)

What is (5-2i)^3 ?
The solution to (5-2i)^3 is 65-142i