finding the roots of a complex number

See the attached file for complete equations --- Use DeMoivre's Theorem to find the indicated power of the following complex numbers: 1. Find the fourth roots of 256(1+3i ) 2. Find all solutions of the equation x3  27i = 0 [please show all the steps, including the algebraic ones] ---

Find zeros of a function

see the attached file.

Using trig identities to cancel and simplify equations

I have included all details on attached file. Please help me get to the final line of the question. Many thanks

Tangent sum formulas

Explain why tan(x + 450 degrees) cannot be simplified using the tnagent sum formulas but can be simplified by using the sine and cosine formulas. (Please show all work).

Trigonometry

What is the difference between a trig equation that is an identity and a trig equation that is not an identity? Provide an example to clarify.