Problems from Complex numbers in the polar form: module and argument

Development:

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

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

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

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

and with the second one,

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

$\alpha =\arctan ({\displaystyle \frac{18}{37}})$

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

Solution:

$4-9i={\sqrt{97}}_{\arctan (-\frac{9}{4})}$ and $37+18i={\sqrt{1693}}_{\arctan (-\frac{18}{37})}$

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