How do you express the complex number in trigonometric form: 1-(sqrt 3)i?
1 Answer
Mar 17, 2018
Explanation:
"to convert to "color(blue)"trigonometric form"
"that is "r(costheta+isintheta)" where"
•color(white)(x)r=sqrt(x^2+y^2)
•color(white)(x)theta=tan^-1(y/x)color(white)(x) -pi < theta <=pi
"here "x=1" and "y=-sqrt3
rArrr=sqrt(1^2+(-sqrt3)^2)=2
theta=tan^-1(-sqrt3)=-pi/3
rArr2(cos(-pi/3)+isin(-pi/3))
=2(cos(pi/3)-isin(pi/3))
rArr1-sqrt3i=2(cos(pi/3)-isin(pi/3))
