Answer: (1 + √5)/2.
- A (1 + √5)/2
- B (√5 - 1)/2
- C (1 + √3)/2
- D 2
Correct answer: A. (1 + √5)/2
Explanation: By triangle inequality |z| - 1/|z| <= |z + 1/z| = 1. Let r=|z|: r - 1/r <= 1. r<sup>2</sup> - r - 1 <= 0. Max r = (1+sqrt(5))/2 (golden ratio).
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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