Answer: 0.
- A 1
- B 2
- C 3
- D 0
Correct answer: D. 0
Explanation: (z<sub>1</sub>+z<sub>2</sub>+z<sub>3</sub>)<sup>2</sup> = z<sub>1</sub><sup>2</sup>+z<sub>2</sub><sup>2</sup>+z<sub>3</sub><sup>2</sup> + 2(z1z2+z2z3+z3z1) = 0. Also |z<sub>1</sub>|=|z<sub>2</sub>|=|z<sub>3</sub>|=1 means 1/z = z-bar. Can show z1z2+z2z3+z3z1 = conj(z<sub>1</sub>+z<sub>2</sub>+z<sub>3</sub>) = 0. So z<sub>1</sub><sup>2</sup>+z<sub>2</sub><sup>2</sup>+z<sub>3</sub><sup>2</sup> = 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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