Answer:
[tex]z = \sqrt{29} ( \cos \: 68 \degree + i \sin 68 \degree)[/tex]
Step-by-step explanation:
The trigonometric form of complex numbers is when the complex number is in polar form.
This is given by
[tex]z = r( \cos \theta + i \sin \theta)[/tex]
where the modulus r is given by
[tex]r = \sqrt{{2}^{2} + {5}^{2} } [/tex]
[tex]r = \sqrt{4 + 25} [/tex]
[tex]r = \sqrt{29} [/tex]
and the argument is given by
[tex] \theta = \tan \:^{ - 1} ( \frac{y}{x}) [/tex]
[tex] \theta = \tan \:^{ - 1} ( \frac{5}{2}) [/tex]
[tex] \theta = 68 \degree[/tex]
The trigonometric form then becomes:
[tex]z = \sqrt{29} ( \cos \: 68 \degree + i \sin 68 \degree)[/tex]
