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Popular >

simplify (4-5i)^3

Solution

simplify

(4 - 5 i)^{3}

Solution

- 236 - 115 i

Solution steps

(4 - 5 i)^{3}

Apply Perfect Cube Formula:

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

(4 - 5 i)^{3} = 4^{3} - 3 \cdot 4^{2} \cdot 5 i + 3 \cdot 4 (5 i)^{2} - (5 i)^{3}

= 4^{3} - 3 \cdot 4^{2} \cdot 5 i + 3 \cdot 4 (5 i)^{2} - (5 i)^{3}

Simplify

4^{3} - 3 \cdot 4^{2} \cdot 5 i + 3 \cdot 4 (5 i)^{2} - (5 i)^{3} : - 115 i - 236

= - 115 i - 236

Rewrite in standard complex form:

- 236 - 115 i

= - 236 - 115 i

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Frequently Asked Questions (FAQ)

What is (4-5i)^3 ?
The solution to (4-5i)^3 is -236-115i