How do you express the complex number in trigonometric form: #1-(sqrt 3)i#?

1 Answer
Mar 17, 2018

Answer:

#2(cos(pi/3)-isin(pi/3))#

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))#