[" Senior Secondary School Mathematics for Class "11],[" EXAMPLE "12" If "1z^(2)-11=|z|^(2)+1" then show that "z" is imaginary."]

If |z^(2)-1|=|z|^(2)+1, then show that z lies on the imaginary axis.

If z^(2) + |z|^(2) = 0 , show that z is purely imaginary.

If |z^2-1|=|z|^2+1 , then show that z lies on the imaginary axis.

Senior Secondary School Mathematics for Class 11 ST-18is the set of all real numbers and Q is the set of all rational numbers then what is the set (RQ) ?

If z=x+iy and |z|=1 , show that (z-1)/(z+1)(z!=-1) is a purely imaginary quantity.

Prove that |z_1+z_2|^2=|z_1|^2, ifz_1//z_2 is purely imaginary.

Given that |z_1+z_2|^2=|z_1|^2+|z_2|^2 , prove that z_1/z_2 is purely imaginary.

Prove that |z_1+ z_2|^2= |z_1|^2+ |z_2|^2 if and only if (z_1/z_2) is purely imaginary.

Prove that |z_1+z_2|^2 = |z_1|^2 + |z_2|^2 if z_1/z_2 is purely imaginary.

If (z-1)/(z+1)(z ne-1) is purely imaginary then show that |z|=1