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

  • -6
Answer is 2

Hope it helps.....

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