How do you write the complex number in trigonometric form $5+2i$ ?

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Answer 1 · 2016-11-19T16:54:43

$5+2i=sqrt29costheta+isqrt29sintheta$ , where $theta=tan^(-1)(2/5)$

A number $a+ib$ can be written in trigonometric form as

$rcostheta+irsintheta$ .

As $rcostheta=a$ and $rsintheta=b$ , squaring and adding them we get $r^2=a^2+b^2$ .

As such for $5+2i$ , $r=sqrt(5^2+2^2)=sqrt(25+4)=sqrt29$

and $costheta=5/sqrt29$ and $sintheta=2/sqrt29$

i.e. $tantheta=2/5$ and $theta=tan^(-1)(2/5)$

Hence in trigonometric form

$5+2i=sqrt29costheta+isqrt29sintheta$ , where $theta=tan^(-1)(2/5)$

How do you write the complex number in trigonometric form 5+2i5+2i?