What is the trigonometric form of  (2+5i) ?

Mar 29, 2016

$\sqrt{29} \angle 1.19$

Explanation:

Any complex number $z = x + i y$ in rectangular form, may be written in polar form $z = r \angle \theta$ by making use of the transformations:
$r = \sqrt{{x}^{2} + {y}^{2}} \mathmr{and} \theta = {\tan}^{- 1} \left(\frac{y}{x}\right) , \theta \in \left[- \pi , \pi\right]$.

So in this particular case, since the complex number is in the first quadrant of the argand plane, we get:

$r = \sqrt{{2}^{2} + {5}^{2}} = \sqrt{29}$

$\theta = {\tan}^{- 1} \left(\frac{5}{2}\right) = 68 , {2}^{\circ} = 1.19 r a d$.

Thus the point may be represented as $\sqrt{29} \angle 1.19$