complex conjugate

What is the complex conjugate of 78.93iw^3+30.48iw^2+iw? How did you find it? thanks.

Equality of Complex Numbers

I sent an attachment of the problem that I was assigned. I am aware that you can't solve the problem for me but I am very confused on how to solve an equality with both an I and an x raised to the 4th power... I know that you must combine the imaginary numbers with other imaginary numbers and real numbers with real numbers but in this problem there doesn't seem to be anything to combine here and I'm stuck. Any help would be appricated. Thanks.

Investments

If I invested $100,000 now at 12% per yr over 15 yrs what if the most I could spend in equal amounts out of the fund each yr? Please also show the formula as to how this was calculated.

complex numbers

Please when working this out can you show every stage in the simplest form to get to the required answer. Problem (also attached): Given that cos x= ... (see attachment) Using ONLY this information, prove that: cosAsinB=1/2[sin(A+B)- sin(A-B)]

Finding roots and solving a quadratic equation

The equation {see attachment} has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of ... {see attachment}