Answer to Question #114733 in Algebra for ANJU JAYACHANDRAN

Question

Obtain the geometric representation of
((5+i)(7+6i))/3+i

Answer 1

((5+i)(7+6i))/(3+i)=(35+30i+7i+6i²)/(3+i) =(35+37i+6(-1))/(3+i) =(29+37i)/(3+i)

(29+37i)/(3+i)*(3-i)/(3-i) =(87-29i+111i-37i²)/(9-i²) =(124+82i)/10 =12.4+8.2i

r=(12.4^2++8.2²)^0.5=14.9

$\alpha$ =arctan(8.2/12.4)=0.58

0.58 radian=33.2°

Answer: z=14.9(cos(33.2°)+isin(33.2°))