Complex numbers in the polar form: module and argument

To write a binomial number in polar form, we must calculate its module and its argument. By means of the formula proposed we have:

$$|4-9i|=\sqrt{4^2+9^2}=\sqrt{16+81}=\sqrt{97}$$

$$\alpha=\arctan(\dfrac{-9}{4})$$

This way: $$ 4-9i= \sqrt{97}_{\arctan(-\frac{9}{4})}$$

and with the second one,

$$|37+18i|=\sqrt{37^2+18^2}=\sqrt{1369+324}=\sqrt{1693}$$

$$\alpha=\arctan(\dfrac{18}{37})$$

This way: $$ 37+18i= \sqrt{1693}_{\arctan(-\frac{18}{37})}$$