Hey, needing some help with these questions:
-2 - i is a solution of the equation z^4 - 5z^2 +4z + 30 = 0. Find the other solutions.
The polynomial P(z) = 2z^3 + az^2 +bz +5, where a and b are real numbers, has 2 - i as one of t's zeroes.
a) Find a quadratic factor of P(z), and hence calculate the real constants a and b
b) Determine the solutions to the equation P(z)=0
Thank you 
Both these questions have a focus on the conjugate root theorem.
Q1. -2-i is a solution and so is -2+i (conj root theorem). So to find the other solutions, expand (z+2+i)(z+2-i), then use this as your divisor for long division of the original polynomial, or use the method of equating coefficients.
Q2. Again conj root theorem, you get p(z)=(az+b)(z-2+i)(z-2-i). You're quadratic factor is the expansion of (z-2+i)(z-2-i). Equate coefficients to solve for a and b, or use long division.