If z−1z+1 is purely an imaginary number and is not equal to -1, then what...
If is purely an imaginary number and is not equal to -1, then what is the value of the modulus of z?
Answer & Explanation
Write . Then:
Multiply top and bottom by :
Since the real part is 0, . The modulus of a complex number is just , so the value of the modulus is 1.
Let where k is any nonzero real.
Solving for z ( using componendo-et-dividendo) we get
Hence (as both numerator and denominaor equals ) Hence