Answer:
- 1
Step-by-step explanation:
z₁ - z₂ = 1 - i - (- 2 + 4i) = 1 - i + 2 - 4i = 3 - 5i, thus
[tex]\frac{3-5i}{1-i}[/tex]
Rationalise the denominator by multiplying the numerator/denominator by the complex conjugate of the denominator
The conjugate of 1 - i is 1 + i, so
[tex]\frac{(3-5i)(1+i)}{(1-i)(1+i)}[/tex]
expand numerator / denominator noting i² = - 1
= [tex]\frac{3-2i-5i^2}{1-i^2}[/tex]
= [tex]\frac{3-2i+5}{1+1}[/tex]
= [tex]\frac{8-2i}{2}[/tex]
= 4 - i
Thus Im [[tex]\frac{z1-z2}{z1}[/tex] ] = - 1
