The complex numbers Z₁ and Z₂ are defined as follows: ²1 6 (cos(4) + i sin(4T)) = Z₂ Calculate = 12 (cos(T) + i sin()) |Z| = 8 = O-3π/5 a = b= ²₁ in polar form, where Z= |Z| (cos(0) + i sin(0)) ²₂ 03π/3 O-TT/5 04T/5 Calculate Z in rectangular form, where Z = a + b i: Write your answers to 2 de places OTT Оπ/2

Find z1z2 in polar form. z1 = 5(cos(170)+i sin(170)) : z2 = (1/2) (cos(10)+i sin(10)

1. Find each of the following. Write each complex number in the form x+ iy. (a) Write (-2 – i) in polar form (approximate the angle to 4 decimal places). (b) e1+(i#/s) »(1+ +()) = = exp 2. Prove the following. (a) 2e*cos(iz) –1 = e2= (b)÷(sin(z)) = cos(z)

Find the product z₁z2 and the quotient 21. Express your answers in polar form. Z2 Z1Z2 = 2₁ = 2(cos(²) + i sin()), Z1 Z1 2212-0 Z2 = 3 (cos() + i sin()) Z₂ = 3