ANSWER
[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]
EXPLANATION
The polar form of a complex number ,
[tex]z = x + yi[/tex]
is given by:
[tex]z = r( \cos( \theta) + i \sin( \theta) )[/tex]
where
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
The given complex number is:
[tex]z = 4 - 10i[/tex]
[tex]r = \sqrt{ {4}^{2} + {( - 10)}^{2} } [/tex]
[tex]r = \sqrt{16 + 100} [/tex]
[tex]r = \sqrt{116} = 2 \sqrt{29} [/tex]
And
[tex]\theta= \tan^{ - 1}(\frac{ y}{x} )[/tex]
[tex]\theta= \tan^{ - 1}(\frac{ - 10}{4} )[/tex]
[tex]\theta= 292 \degree[/tex]
Hence the polar form is :
[tex]r = 2 \sqrt{29} ( \cos(292 \degree) + \sin(292 \degree)) [/tex]
