Answer: 2.
- A 0
- B 1
- C 2
- D Infinitely many
Correct answer: C. 2
Explanation: z=z̄ means the imaginary part of z is 0, so z must be real. Combined with |z|=1: z∈R and |z|=1 gives z=1 or z=-1. Check: |1|=1✓, 1̄=1✓; |-1|=1✓, (-1̄)=-1✓. Exactly 2 solutions. Answer: 2 complex numbers
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
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