Mathematics - Complex Number Question with Solution | TestHub

(I) $\left|{\mathrm{z}}_1-{\mathrm{z}}_2\right|=\left|{\mathrm{z}}_1\right|+\left|{\mathrm{z}}_2\right|$

(P) ${\theta }_1-{\theta }_2=\frac{\pi }{2}$

(II) ${\left|z_1-z_2\right|}^2={\left|z_1\right|}^2+{\left|z_2\right|}^2$

(Q) ${\theta }_1-{\theta }_2=-\frac{\pi }{2}$

(III) $\left|{\mathrm{z}}_1+{\mathrm{z}}_2\right|=\left|{\mathrm{z}}_1-{\mathrm{z}}_2\right|$

(R)

(IV) $\left|{\mathrm{z}}_1+{\mathrm{z}}_2\right|=\left|{\mathrm{z}}_1\right|+\left|{\mathrm{z}}_2\right|$

(S)

(T)