Find [9(cos 20◦ + isin 20◦)]/[5(cos 75◦ + isin 75◦)] and write the result in trigonometric form.

Question

jim_thompson5910 · Answer

[9( cos(20) + i*sin(20) )]/[5( cos(75) + i*sin(75) )]


[9*e^(20i)]/[5*e^(75i)]


(9/5)*e^(20i-75i)


(9/5)*e^(-55i)


(9/5)*1/(e^(55i))


(9/5)*[1/( cos(55) + i*sin(55) )]


(9/5)*[1/( cos(55) + i*sin(55) )][( cos(55) - i*sin(55) )/( cos(55) - i*sin(55) )]


(9/5)*[( cos(55) - i*sin(55) )/( cos^2(55) - i^2*sin^2(55) )]


(9/5)*[( cos(55) - i*sin(55) )/( cos^2(55) + sin^2(55) )]


(9/5)*[( cos(55) - i*sin(55) )/( 1 )]


(9/5)*( cos(55) - i*sin(55) )