Question

The multiplicative inverse of z = 1+i is a) 1+i b) 1-i c) 1/2+i/2 d) 1/2-1/2​

Answer 1

we know multiplicative inverse of complex number z is z^-1

z^-1=1/(1+i)

z^-1=(1/1+i)

z^-1=(1/1+I)(1-i/1-i)

z^-1=(1-i)/(1-i^2)

z^-1=(1-i)/{1-(-1)} we know i^2=-1

z^-1=(1-i)/2

z^-1=(1/2)-(i/2)