Show that :
`| z_(1)z_(2)| = | z_(1)||z_(2)|`

If the complex number Z_(1) and Z_(2), arg (Z_(1))- arg(Z_(2)) =0 . then show that |z_(1)-z_(2)| = |z_(1)|-|z_(2)| .

If for complex numbers z_(1) and z_(2)arg(z_(1))-arg(z_(2))=0, then show that |z_(1)-z_(2)|=|z_(1)|-|z_(2)||

For any two complex numbers z_(1) and z_(2), prove that |z_(1)+z_(2)| =|z_(1)|-|z_(2)| and |z_(1)-z_(2)|>=|z_(1)|-|z_(2)|

If z_(1)=2+3i and z_(2)=3+i , plot the number z_(1)+z_(2) . Also show that: |z_(1)|+|z_(2)|gt|z_(1)+z_(2)| .

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

Prove that |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2),quad if z_(1)/z_(2) is purely imaginary.

If z_(-)1 and z_(-)2 are any two complex numbers show that |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2|z_(1)|^(2)+2|z_(2)|^(2)

If Z_(1)=1+i and Z_(2)=2+2i , then which of the following is not true. (A) |z_(1)z_(2)|=|z_(1)||z_(2)| (B) |z_(1)+z_(2)|=|z_(1)|+|z_(2)| (C) |z_(1)-z_(2)|=|z_(1)|-|z_(2)| (D) |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|)