For a complex number #z=a+bi#, we can rewrite it in the form #z=r(costheta+isintheta)#, where #r=sqrt(a^2+b^2)# and #theta=tan^(-1)(b/a)#
#z_1=2+i#
#r_1=sqrt(2^2+1^2)=sqrt(5)#
#theta_1=tan^(-1)(1/2)#
#z_1=sqrt(5)(cos(tan^(-1)(1/2))+isin(tan^(-1)(1/2))#
#z_2=3+7i#
#r_2=sqrt(3^2+7^2)=sqrt(58)#
#theta_2=tan^(-1)(7/3)#
#z_2=sqrt(5)(cos(tan^(-1)(7/3))+isin(tan^(-1)(7/3))#
#z_1/z_2=r_1/r_2(cos(theta_1-theta_2)+isin(theta_1-theta_2))#
#z_1/z_2=sqrt(5)/sqrt(58)(cos(tan^(-1)(1/2)-tan^(-1)(7/3))+isin(tan^(-1)(1/2)-tan^(-1)(7/3)))#
#~~sqrt(290)/58(cos(-40.24)+isin(-40.24))#
Since #cos(x)=cos(-x)# and #sin(-x)=-sin(x)#
#=sqrt(290)/58(cos(40.24)-isin(40.24))#
