Question

Find the multiplicative inverse of the complex number 1+ i​

Answer 1

Let z=x+iy be multiplication inverse of 1−i

then we must have

(x+iy)(1−i)=1

x−ix+iy+y=1

x+y=1 and x−y=0

put x=y we have x=y

2y=1 y=

2

1

,x=

2

1

Hence z=x+iy=

2

1

+

2

i

Answer 2

-1-I is your answer