Q7

Which of the following statements about complex numbers is true?

A. For all real numbers $x,y,\theta$ with $x\ne0$, $\tan\theta=\frac yx\Rightarrow x+iy=re^{i\theta}$ for some real number $r$.
B. For all non-zero complex numbers $z_1,z_2$, if $\operatorname{Arg}(z_1)=\theta_1$ and $\operatorname{Arg}(z_2)=\theta_2$, then $\operatorname{Arg}(z_1z_2)=\theta_1+\theta_2$.
C. For all real $r_1,r_2,\theta_1,\theta_2$ with $r_1,r_2>0$, $r_1e^{i\theta_1}=r_2e^{i\theta_2}\Rightarrow r_1=r_2$ and $\theta_1=\theta_2$.
D. For all real $x,y,r,\theta$ with $r>0$ and $x\ne0$, $x+iy=re^{i\theta}\Rightarrow\theta=\arctan(y/x)$.