# How do you convert # -7-7sqrt3i# to polar form?

##### 1 Answer

Sep 13, 2017

#### Explanation:

#"to convert from "color(blue)"cartesian to polar form"#

#"that is "x+yito(x,y)to(r,theta)" using"#

#•color(white)(x)r=sqrt(x^2+y^2)#

#•color(white)(x)theta=tan^-1(y/x)#

#"here "x=-7" and "y=-7sqrt3#

#rArrr=sqrt((-7)^2+(-7sqrt3)^2)#

#color(white)(rArrr)=sqrt(49+147)=sqrt196=14#

#"since "-7-7sqrt3i" is in the third quadrant we must"#

#"ensure that "theta" is in the third quadrant"#

#theta=tan^-1(sqrt3)=pi/3larrcolor(blue)"related acute angle"#

#rArrtheta=(pi+pi/3)=(4pi)/3larrcolor(blue)" in third quadrant"#

#rArr(-7,-7sqrt3)to(14,(4pi)/3)#