Express z = 2 + 2i√3 in polar form.

To express a complex number in polar form, we use the formula z = r(cos θ + i sin θ), where r is the magnitude of z and θ is the argument of z.

Step 1: Calculate the magnitude r The magnitude r of a complex number z = x + yi is given by r = √(x² + y²). For z = 2 + 2i√3, we have x = 2 and y = 2√3. So, r = √((2)² + (2√3)²) = √(4 + 12) = √16 = 4.

Step 2: Calculate the argument θ The argument θ of a complex number z = x + yi is given by θ = atan(y/x). For z = 2 + 2i√3, we have x = 2 and y = 2√3. So, θ = atan(2√3/2) = atan(√3) = π/3.

Step 3: Write the polar form Now we can write z in polar form using the formula z = r(cos θ + i sin θ). So, z = 4(cos(π/3) + i sin(π/3)).

So, the polar form of z = 2 + 2i√3 is z = 4(cos(π/3) + i sin(π/3)).