How do you write the complex number in trigonometric form #6-7i#?
1 Answer
Sep 3, 2017
Explanation:
#"to convert from"color(blue)" complex to trig. form"#
#"that is "x+yitor(costheta+isintheta)" using"#
#•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=6" and "y=-7#
#rArrr=sqrt(6^2+(-7)^2)=sqrt85#
#6-7i" is in the fourth quadrant so we must ensure that "theta#
#"is in the fourth quadrant"#
#rArrtheta=tan^-1(7/6)=0.862larrcolor(red)" related acute angle"#
#rArrtheta=-0.862larrcolor(red)" in fourth quadrant"#
#rArr6-7i=sqrt85(cos(-0.862)+isin(-0.862))#
#[cos(-0.862=cos(0.862);sin(-0.862)=-sin(0.862)]#
#rArr6-7i=sqrt85(cos(0.862)-isin(0.862))#
