Question

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

Answer 1

`z = √(29) ( \cos \: 68 \degree + i \sin 68 \degree)`

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 = √(4 + 25)`

`r = √(29)`

and the argument is given by

`\theta = \tan \:^( - 1) ( (y)/(x))`

`\theta = \tan \:^( - 1) ( (5)/(2))`

`\theta = 68 \degree`

The trigonometric form then becomes:

`z = √(29) ( \cos \: 68 \degree + i \sin 68 \degree)`