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# Find the product of z_{1} and z_{2}, where z_{1} = 8(cos40° + i sin40°) and z_{2} = 4(cos135° + i sin135°).

**Solution:**

To find the product of the z_{1} and z_{2}, we will use the rules of complex numbers.

z_{1} = r_{1} (cosθ + i sinθ)

z_{2} = r_{2}(cosϕ + i sinϕ )

⇒ z_{1} × z_{2} = r_{1} × r_{2} (cos (θ + ϕ) + i sin (θ + ϕ)) --- equation(1)

Using equation(1),

r_{1} = 8, r_{2} = 4

θ = 40°, ϕ = 135°

z_{1} × z_{2} = 8 × 4 (cos(40° + 135°) + i sin(40° + 135°))

z_{1} × z_{2} = 32 (cos(175°) + i sin(175°))

## Find the product of z_{1} and z_{2}, where z_{1} = 8(cos40° + i sin40°) and z_{2} = 4(cos135° + i sin135°).

**Summary:**

The product of z_{1} and z_{2}, where z_{1} = 8(cos40° + i sin40°) and z_{2} = 4(cos135° + i sin135°) is 32 (cos(175°) + i sin(175°)).

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