Question

If z1 and z2 are 1-i and -2+4i respectively find Im[z1-z2/z1]

Answer 1

Answer:

- 1

Step-by-step explanation:

z₁ - z₂ = 1 - i - (- 2 + 4i) = 1 - i + 2 - 4i = 3 - 5i, thus

$\frac{3-5i}{1-i}$

Rationalise the denominator by multiplying the numerator/denominator by the complex conjugate of the denominator

The conjugate of 1 - i is 1 + i, so

$\frac{(3-5i)(1+i)}{(1-i)(1+i)}$

expand numerator / denominator noting i² = - 1

= $\frac{3-2i-5i^2}{1-i^2}$

= $\frac{3-2i+5}{1+1}$

= $\frac{8-2i}{2}$

= 4 - i

Thus Im [$\frac{z1-z2}{z1}$ ] = - 1