How do you write the complex number in trigonometric form #sqrt3+i#?

1 Answer
Douglas K.
Sep 25, 2016

For a number of form, #a + bi#, the form #A(cos(theta) + isin(theta))# is obtained by using #A = sqrt(a² + b²# and #theta = tan^-1(b/a)# (adjust #theta# for the proper quadrant)

Explanation:

#A = sqrt(sqrt3^2 + 1^2#

#A = 2#

#theta = tan^-1(1/sqrt3)#

#theta = pi/6#

Because the signs of "a" and "b" are positive, we do not adjust the quadrant.

#sqrt3 + i = 2(cos(pi/6) + isin(pi/6))#

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