Reprenesent the complex number 5/2(square root of 3-i) graphically and find its trigonometric form.
first find the number 3-i in polar form
r = √(3^2 + 1^2) = √10
tanØ = (-1/3) , where Ø is in IV
Ø = 341.565°
so 3-i = √10(cos 341.565 + isin341.565)
then
(3-i)^(1/2) = [ (√10)(cos 341.565 + isin341.565) ]^(1/2)
= √10^(1/2)(cos 170.7825 + isin 170.7825) by DeMoirve's Theorem
finally (5/2)√(3-1)
= 5(10)^(1/4)/2)[cos 170.8° + isin 170.8°)
or
5(10)^(1/4) cis 170.8°