how to conert rectangle form 2+3i to polar form :
$$z = x + y i \quad | \quad z = 2 + 3i$$
polar: $$x = r*\cos{(\phi)} \quad and \quad y = r*\sin{(\phi)}$$
set into z = x + yi: $$z = r*\cos{(\phi)}+ r*\sin{(\phi)}i = r \left[ \cos{(\phi)}+ \sin{(\phi)}i \right] = r \left[ \cos{(\phi)}+ i\sin{(\phi)} \right]$$
r: $$r=\sqrt{x^2+y^2} \quad | \quad r = \sqrt{2^2+3^2} = \sqrt{4+9} = \sqrt{13}$$
$$\phi$$ : $$\phi = \tan^{-1}{ ( \frac{y}{x} )} \quad | \quad \phi = \tan^{-1}(\frac{3}{2}) = 56.3099324740\ensurement{^{\circ}}$$
z(polar): $$z=r \left[ \cos{(\phi)}+ i\sin{(\phi)} \right] \quad | \quad z = \sqrt{13} \left[ \cos{(56.3099324740\ensurement{^{\circ}})}+ i*\sin{(56.3099324740\ensurement{^{\circ}})} \right]$$
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