What is (2+isqrt(3))^3 ?

The solution to (2+isqrt(3))^3 is -10+9sqrt(3)i

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simplify (2+isqrt(3))^3

simplify

(2 + i 3)^{3}

- 10 + 93 i

Solution steps

(2 + i 3)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

2^{3} + 3 \cdot 2^{2} i 3 + 3 \cdot 2 (i 3)^{2} + (i 3)^{3} : 93 i - 10

= 93 i - 10

Rewrite in standard complex form:

- 10 + 93 i

= - 10 + 93 i

(t - 3) (t + 3)

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7 \cdot 8

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