Find the product of z₁ and z₂, where z₁ = 2(cos80° + i sin80°) and z₂ = 9(cos 110° + i sin110°)

Solution:

To find the product of the z₁ and z₂, we will use the rules of complex numbers.

z₁ = r₁(cosθ + i sinθ)

z₂ = r₂(cosϕ + i sinϕ )

⇒ z₁ × z₂ = r₁ × r₂ (cos(θ + ϕ ) + i sin(θ + ϕ)) --- equation(1)

Using equation(1),

r₁ = 2, r₂ = 9

θ = 80°, ϕ = 110°

z₁ × z₂ = 2 × 9 (cos(80° + 110°) + i sin(80° + 110°))

z₁ × z₂ = 18 (cos(190°) + i sin(190°))

Find the product of z₁ and z₂, where z₁ = 2(cos80° + i sin80°) and z₂ = 9(cos110° + i sin110°)

Summary:

The product of z₁ and z₂, where z₁ = 2(cos80° + i sin80°) and z₂ = 9(cos110° + i sin110°) is 18 (cos(190°) + i sin(190°)).