Question

solve for z writing the answer in polar form:
#1 z=(3,115 degrees)*(4,290 degrees)

#2 (8,50 degrees)* z=(6,172 degrees)

Answer 1

Multiply the magnitudes and add the angles to multiply
This comes from z = x + i y = r e^(i T)
here we have
3 e^i 115 * 4 e^i 290

You know to multiply 3*4 to get 12
now e^a * e^b = e^(a+b) (rules of exponents)

so we have 12 e^i(115+290) = 12 e^i 405
but 405 - 360 = 45
so we really have
modulus = 12
argument = 45 degrees

Answer 2

(6,172 degrees)
----------------
(8,50 degrees)

to divide, divide moduli, subtract angles (same discussion as for multiplication)
(.75) e^i (122)

by the way, the angles are generally expressed in radians for this notation.