If z1 = 3+2i, z2= 4-i, z3=1+i, find and simplify the following: a) z1 + z2, b) z2 x z3, c)z2* (complex conugate of z2), d) z2/z3.

(a) For part a, simply add the real terms together and the imaginary terms together. z₁+z₂ = (3+2i)+(4-i) = 7+i b).     

(b) For part b, multiply the brackets out, remembering that i²=-1. z₂ x z₃ = (4-i)(1+i) = 4 - i + 4i + 1 = 5+3i.      

(c) To find the complex conjugate, you just need to change the sign of the imaginary term. z₂* = 4+i .     

(d) To find this, you need to use all of the previous skills. To simplify a complex fraction, you need to multiply both the numerator and denominator by the complex conjugate of the denominator. This results in the denominator having no imaginary terms. z₂/z₃ = (4-i)/(1+i) = (4-i)(1-i)/(1+i)(1-i) = (4-i-4i-1)/(1+i-i+1) = (3-5i)/2 = 3/2 + 5/2i.