We need to evaluate and simplify 4i^{-32} where i = √-1

Since the power you entered of -32 is > 4, then we see how many i^{4} factors we can factor out: i^{-32} = (i^{4})^{-8}

First calculate i^{4}: i^{4} = i * i * i * i i^{4} = √-1 * √-1 * √-1 * √-1 i^{4} = (√-1)^{2} * (√-1)^{2} i^{4} = -1 * -1 i^{4} = 1

Now substitute our i^{4} value back in the equation: i^{ -32} = (1)^{-8} <--- i^{4} = 1 i^{ -32} = 1/(1^{8}) <--- Convert negative power by taking 1 over the term i^{ -32} = 1/1 i^{ -32} = 1

Multiply our result by our coefficient of 4 4(1) = 4