if z1= 1-i and z2= -2+4i find i'm(z1*z2/z1) maths class 11

here z₁=1-i and z₂=-2+4i,

now (z₁*z₂/z₁)=(1-i)(-2+4i)/(1-i)

=(-2+4i+2i-4i²)/(1-i)

=(-2+6i-4(-1))/(1-i) {since i²=-1}

=(-2+6i+4)/(1-i)

=(2+6i)/(1-i)

now by rationalising i.e. multiplyind and dividing by (1+i)

=(2+6i)*(1+i)/((1-i)*(1+i)

=(2+2i+6i+6i²)/(1²-i²) {since (a+b)(a-b)=a²-b²}

=(2+8i+6(-1))/(1-(-1)) {since i²=-1}

=(2+8i-6)/(1+1)

=(-4+8i)/2

=2(-2+4i)/2

=-2+4i

now img(z₁*z₂/z₁)=4 as imaginary part is equal to 4