The complex numbers Z and W are given by Z=3+3i and W=6-i. Giving your answers in the form of x+yi and showing how you clearly obtain them, find: i) 3Z-4W ii) Z*/W

i) 3Z-4WFor this question it is just the matter of substituting the complex numbers of Z and W into the equation. So, 3(4+3i)-4(6-i). Then multiply out the brackets to get 12+9i-24+4i. Finally simply to get -12+13i.This question is worth two marks and you get awarded one mark for the real part and one mark for the imaginary part.ii)Z*/WIn this question we are asked to divide the complex conjugate of Z by W. Z* = 4-3i, so Z*/W = *4-3i)/(6-i).To solve this we must make the denominator real. This is similar to rationalizing surds, the trick here is to multiply by the conjugate, so we get ((4-3i)x(6+i))/((6-i)(6+i))No we carefully multiply out to get (24+4i-18i-3i^2)/(36-i^2). The important part of multiplying by the complex conjugate is so that the complex part of the denominator cancels. Now we simply to get (27-14i)/37 remembering that i^2=-1Finally the last step is to write the answer in the form of x+yi to ensure we get full marks which is simply (27/37)-(14/37)iThis question was worth 4 marks. You get one mark for writing down the conjugate of Z correctly, you got a method mark for multiplying by the conjugate of W and then two accuracy marks for finding the real and imaginary parts.