Answer: 3.
- A 1
- B 2
- C 3
- D Infinitely many
Correct answer: C. 3
Explanation: z² = −|z| is real and ≤ 0, forcing z purely imaginary or zero. Writing z = iy gives −y² + |y| = 0, so |y| = 0 or 1. Solutions: 0, i, −i.
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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