Question

The complex number z=12+5i can also be written as z=r(cosθ+isinθ)

, where
Select one:

Answer 1

Answer:

$z = 13( \cos( \alpha ) ) + i \sin( \alpha ) )$

Step-by-step explanation:

$|z| = \sqrt{ {12}^{2} + {5}^{2} } = \sqrt{144+ 25} = \sqrt{169} = 13 \\ \\ \tan( \alpha ) = \frac{5}{12} \\ \\ \cos( \alpha ) = \frac{12}{13} \\ \\ \sin( \alpha ) = \frac{5}{13} \\ \\ z = 13( \cos( \alpha ) ) + i \sin( \alpha ) )$