Question

If z1=(2,5),z2=(-1,4) then z1/z2=

Answer 1

Given : Z₁ = (2, 5) and Z₂ = (-1,4)

To find : find Z₁/Z₂

solution : This question is based on complex numbers.

Z₁ = (2,5) = 2 + 5i

Z₂ = (-1, 4) = -1 + 4i

so, Z₁/Z₂ = (2 + 5i)/(-1 + 4i)

= (2 + 5i)(-1 - 4i)/(-1 + 4i)(-1 - 4i)

= {2(-1 - 4i) + 5i(-1 - 4i)}/{(-1)² - (4i)²}

= {-2 - 8i - 5i - 20i²}/{1 - 16i²}

= {-2 - 13i - 20 × -1}/{1 - 16 × -1} [ we know, i² = -1]

= (18 - 13i)/17

= 18/17 + (-13/17)i

therefore, Z₁/Z₂ = (18/17, -13/17)