How do you write the complex number in trigonometric form #1+3i#?

1 Answer
Jim G.
Sep 18, 2016

#sqrt10(cos(1.249)+isin(1.249))#

Explanation:

To convert from #color(blue)"complex to trigonometric form"#

That is #x+yitor(costheta+isintheta)#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(r=sqrt(x^2+y^2))color(white)(a/a)|)))#

and #color(red)(bar(ul(|color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|))) (-pi < theta <= pi)#

here x = 1 and y = 3

#rArrr=sqrt(1^2+3^2)=sqrt10#

Now 1 + 3i is in the 1st quadrant so #theta# must be in the 1st quadrant.

#theta=tan^-1(3)=1.249" rad" larr" in 1st quad."#

#rArr1+3itosqrt10(cos(1.249)+isin(1.249))#

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