Question

1
(a) If \<,/ = 1231 = 1 then prove
= 1 then prove that lz, + zz
Z Z2​

Answer 1

Let z=x+iy

z

2

−1=(x

2

−y

2

−1)+2ixy

∣z∣

2

+1=x

2

+y

2

+1

Hence

∣z

2

−1∣=∣z∣

2

+1

(x

2

−y

2

−1)

2

+4x

2

y

2

=(x

2

+y

2

+1)

2

4x

2

y

2

=(x

2

+y

2

+1)

2

−(x

2

−y

2

−1)

2

4x

2

y

2

=(2x

2

)(2y

2

+2)

x

2

y

2

=(x

2

)(y

2

+1)

x

2

y

2

=x

2

y

2

+x

2

x

2

=0

x=0

Hence, z lies on imaginary axis.