 In this video, we provide the solution to question number eight from the practice final exam for math 1060 And we're asked to find the product of Cosine of 15 degrees plus I sign a 15 degrees squared and we want to write this complex number in standard form So it should look something like a plus bi a real part plus an imaginary part Now I notice here that this complex number is already in polar form So this is equivalent to e to the i times 15 degrees like so and you're squaring this Right that the modulus of this complex number is one So the fact that this is in polar form makes the calculation much more straightforward This is gonna be e to the i we actually multiply the exponent when we have these nested exponents like so so this is actually gonna be i times 30 degrees like so which is the same thing as cosine of 30 degrees plus i sine of 30 degrees like so cosine of 30 is going to be root 3 over 2 and Sign of 30 is gonna be one-half. So you get root 3 over 2 plus i Over 2 and so then we would select choice f as our correct answer Notice we didn't actually need to know what cosine of 15 degrees or a sign of 15 degrees was We didn't have a calculator So we could have possibly memorized that using a half angle identity or angle difference or whatever But it turns out using DeMauvera's DeMauvera's theorem makes this whole much easier because when you multiply together Complex numbers in polar form. We're just gonna add together their arguments