1. Given the complex numbers z1 = 2 − i and z2 = 1 + i.?

1. Given the complex numbers z1 = 2 − i and z2 = 1 + i.


(a) Find z3 = z1 z2.


(b) Find z4 = z1/z2


.(note zk is z subscript k and rk is r subscript k)


(c) Express each zk in polar form zk = rk (cos θk + i sin θk)


; − π%26lt; θk ≤ π for k = 1, 2, 3 and 4.


(d) (i) Show r3 = r1 r2.


(ii) Show r4 = r1/r2


.


(iii) Show θ3 = θ1 + θ2.


(iv) Show θ4 = θ1 − θ2.


(e) Plot the complex numbers zk for k = 1, 2, 3 and 4 in the complex plane.

1. Given the complex numbers z1 = 2 − i and z2 = 1 + i.?
z1 = 2 − i


z2 = 1 + i


z3= 2*1+2i -i -i^2= 3+i


z4 = (2-i)(1-i)/(1+i)^2 = (1-3i)/(2)





You should be able to work out the rest.


r^2= x^2+y^2


tan(theta) = y/x


r = |x+yi| sqrt(x^2+y^2)
Reply:Use properties of complex numbers to solve this problem.


(a) z3=(2-i)(1+i)=3+i


(b) z4=(2-i)/(1+i)=(1/2)(1-3i)


(c) Find the absolute value of the complex vector and the angle.


The rest of the problems should be easy.


Give it a try......