Answer to Question #7900 in Trigonometry for Mercedes Jones

Question

Write the complex number in trigonometric form, using degree measure for the argument of -0.85 - 6.01i

Answer 1

So we need to find module and argument
module r=sqrt(0.85^2+6.01^2)=sqrt(0,7225+36,1201)=sqrt(36,8426)=6,07
alpha=tan^-1(y/x)=tan^-1(-6.01/-0.85)=tan^-1(7,07)=81.9 degrees
given complex number is in teh 3rd quadrant so argument = pi+81.9
so -0.85 - 6.01i=6.07(cos(pi+81.9 )+i sin(
pi+81.9 ))