Answer: Purely real.
- A Purely imaginary
- B Purely real
- C Of modulus 1
- D Equal to the conjugate of z
Correct answer: B. Purely real
Explanation: Since |z| = 1, 1/z = z̄, so 1 + z² = z(z̄ + z) = z·2Re(z). Then z/(1+z²) = 1/(2Re(z)), which is real.
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
Read the full Complex Numbers and Quadratic Equations notes →