What is the simplified form of : [(-1+ i*sqrt(3))^3] / 2  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We need to find the value of (-1+ i *sqrt(3))^3 / 2

To solve this we use (a + b)^3 = a^3 + 3a^b + 3ab^2 + b^3 and the fact that i*2 = -1.

(-1+ i *sqrt(3))^3 / 2

=> (1/2)[ (-1)^3 + (i*sqrt 3)^3 + 3*(-1)(i*sqrt 3)^2 + 3*(-1)^2 * i*sqrt 3]

=> (1/2)[ -1 - i*3*sqrt 3 + 3*3 + 3*i*sqrt 3]

=> (1/2)*8

=> 4

The required result is 4

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