# Answer to Question #7900 in Trigonometry for Mercedes Jones

Question #7900

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

Expert's answer

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

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 ))

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 degreesgiven 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 ))

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