complex numbers

Question 1

z is completely real

Answer 1

y=0

Question 2

z is completely imaginary

Answer 2

x=0

Question 3

z1z2=

Answer 3

(x1x2-y1y2)+i(x1y2+x2y1)

Question 4

reciprocal of z

Answer 4

1/z=z(conjugate)//|z|^2

Question 5

the argument of z is

Answer 5

@=tan-1(y/x)

Question 6

principal value of argument

Answer 6

@, π-@, - π+@, -@

Question 7

polar form

Answer 7

z=r(cos@+isin@) where r=|z| and @=arg(z)

Question 8

eulers form

Answer 8

z=re^i@, r=|z| @=arg(z)

Question 9

cube root of unity

Answer 9

are 1,w,w^2

Question 10

value of w

Answer 10

w=-1+√3 i/2 w^2=-1-√3 i/2

Question 11

properties of cube root

Answer 11

1+w+w^2=0

w^3=1