Expanding Binomials: Simplifying Complex Expressions

[killersanta]

Homework Statement

by expanding the binomial show that ( (Sqtroot(3)/2) + (1/2)i )^4 = ( (-1/2) + (sqroot(3)/2)i )

The Attempt at a Solution

I'm stuck, I now ( (Sqtroot(3)/2) + (1/2)i )^4 = ( (9/16) + (1/16)i )

But that's all I got, don't know the next steps.

 

[Mark44]

Homework Statement

by expanding the binomial show that ( (Sqtroot(3)/2) + (1/2)i )^4 = ( (-1/2) + (sqroot(3)/2)i )

The Attempt at a Solution

I'm stuck, I now ( (Sqtroot(3)/2) + (1/2)i )^4 = ( (9/16) + (1/16)i )

But that's all I got, don't know the next steps.

It looks like you are saying that (a + b)⁴ = a⁴ + b⁴. Or that (a + bi)⁴ = a⁴ + b⁴i. Neither is true at all. If you know about the Binomial Theorem you can get the coefficients. For example, (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴.

If you don't know about that theorem you can just expand the left side by the square of that binomial, and then multiplying the result by itself. That will give you the fourth power of your binomial.