Problems 43 through 47 pertain to the solution of differential equations with complex coefficients.

(a) Use Euler's formula to show that every complex number can be written in the form re^iθ, where r ≧ 0 and -π < θ ≦ π.

(b) Express the numbers 4, -2, 3i, 1+ i, and -1 + i√3 in the form re^iθ.

(c) The two square roots of re^iθ are ± √re^iθ/2. Find the square roots of the numbers 2 - 2i √3 and -2 + 2i √3.