If $$z1=z2=1$$,$$z1z2$$≠−$$1$$ and $$z=z1+z21+z1z2$$

Correct option is 1z is a purely real number

Questions

If $|z_{1}| = |z_{2}| = 1, z_{1} z_{2} \neq - 1$ and $z = \frac{z_{1} + z_{2}}{1 + z_{1} z_{2}}$

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z is a purely real number

z is a purely imaginary number

|z| = 1

none of these

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detailed solution

Correct option is A

z¯=z¯1+z¯21+z¯1z¯2=1/z1+1/z21+1/z1z2=z1+z21+z1z2=zThus, z is purely real.

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If z1=z2=1,z1z2≠−1 and z=z1+z21+z1z2

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If $|z_{1}| = |z_{2}| = 1, z_{1} z_{2} \neq - 1$ and $z = \frac{z_{1} + z_{2}}{1 + z_{1} z_{2}}$