Answer: 0.
- A 1
- B i
- C 0
- D (1 + i)/2
Correct answer: C. 0
Explanation: |z−1| = |z+1| gives Re(z) = 0, so z = iy. Then |z+1| = |z−i| gives 1 + y² = (y−1)², so y = 0. Hence z = 0.
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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