Remember that we can write every complex number in the form:
where x is the real part of z, and y is the imaginary part of z.
If z = 2 (or z = 2 + i*0), then the real part of z is 2, and the imaginary part of z is 0 (there's no imaginary part of this z). So:
Now, the question wants us to rewrite z in polar form:
If you distribute the r into the parenthesis, you'll end up with:
In the above expression, the real part of z is in the first term, and the imaginary part in the second term:
- x = r cos θ,
- y = r sin θ.
Now we can equate our expressions for x and y:
- 2 = r cos θ,
- 0 = r sin θ.
We have here a system of two equations with two unknowns. Solve for r and θ using any method you like. Best of luck!