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.
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