Final answer:
To find the product of complex numbers, multiply the real parts and imaginary parts separately and combine them. The product of z₁=3(cos(π/4)+i sin(π/4)) and z₂=2(cos(3π/4)+i sin(3π/4)) is 6√2(cos(π/2) + i sin(π/2)).
Step-by-step explanation:
To find the product of complex numbers, we multiply the real parts and imaginary parts separately and then combine them.
Given z₁=3(cos(π/4)+i sin(π/4)) and z₂=2(cos(3π/4)+i sin(3π/4)), we can calculate:
Real part of z₁z₂ = 3 × 2 × cos(π/4 + 3π/4)
Imaginary part of z₁z₂ = 3 × 2 × sin(π/4 + 3π/4)
Simplifying these expressions, we get:
Real part of z₁z₂ = 6√2 × cos(π/2)
Imaginary part of z₁z₂ = 6√2 × sin(π/2)
Therefore, the product z₁z₂ is 6√2(cos(π/2) + i sin(π/2)).