Answer: An arc of the circle x² + y² = 1.
- A The line x = 0
- B An arc of the circle x² + y² = 1
- C A parabola
- D The entire real axis
Correct answer: B. An arc of the circle x² + y² = 1
Explanation: The segment joining −1 and 1 subtends a right angle at z, so z lies on the circle with that segment as diameter, x² + y² = 1 (the arc where the angle is +π/2).
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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