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Popular >

simplify (z+i)^3

Solution

simplify

(z + i)^{3}

Solution

(z^{3} - 3 z) + (3 z^{2} - 1) i

Solution steps

(z + i)^{3}

Apply Perfect Cube Formula:

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

(z + i)^{3} = z^{3} + 3 z^{2} i + 3 z i^{2} + i^{3}

= z^{3} + 3 z^{2} i + 3 z i^{2} + i^{3}

3 z i^{2} = - 3 z

i^{3} = - i

= z^{3} + 3 z^{2} i - 3 z - i

Rewrite in standard complex form:

(z^{3} - 3 z) + (3 z^{2} - 1) i

= (z^{3} - 3 z) + (3 z^{2} - 1) i

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Frequently Asked Questions (FAQ)

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