Represent √3+i in polar form?

2 Answers
Oct 21, 2017

See Explanation

Explanation:

Tony B

Oct 21, 2017

sqrt(3) + i = 2(cos(pi/6) + isin(pi/6))3+i=2(cos(π6)+isin(π6))

Explanation:

Let sqrt(3) + i = z3+i=z

Modulus of zz:

|z| = sqrt(sqrt(3)^2 + 1^2) = sqrt(4) = 2 = r|z|=32+12=4=2=r

Argument of zz:

arctan(1/sqrt(3)) = pi/6 = thetaarctan(13)=π6=θ

z = r(cos(theta) + isin(theta)) = 2(cos(pi/6) + isin(pi/6))z=r(cos(θ)+isin(θ))=2(cos(π6)+isin(π6))