Question

Z=2+5i. Convert the complex number to trigonometric form.

Answer 1

Answer:

$z = \sqrt{29} ( \cos \: 68 \degree + i \sin 68 \degree)$

Step-by-step explanation:

The trigonometric form of complex numbers is when the complex number is in polar form.

This is given by

$z = r( \cos \theta + i \sin \theta)$

where the modulus r is given by

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

$r = \sqrt{4 + 25}$

$r = \sqrt{29}$

and the argument is given by

$\theta = \tan \:^{ - 1} ( \frac{y}{x})$

$\theta = \tan \:^{ - 1} ( \frac{5}{2})$

$\theta = 68 \degree$

The trigonometric form then becomes:

$z = \sqrt{29} ( \cos \: 68 \degree + i \sin 68 \degree)$