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Popular >

simplify (i+m)^3

Solution

simplify

(i + m)^{3}

Solution

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

Solution steps

(i + m)^{3}

Apply Perfect Cube Formula:

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

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

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

i^{3} = - i

3 i^{2} m = - 3 m

3 i m^{2} = 3 m^{2} i

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

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

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