Answer: z₁ = 0 or z₂ = 0.
- A z₁ = z₂
- B z₁ = 0 and z₂ = 0
- C z₁ = 0 or z₂ = 0
- D z₁ = −z₂
Correct answer: C. z₁ = 0 or z₂ = 0
Explanation: Complex numbers form a field (no zero divisors). Proof: if z₁z₂=0 and z₁≠0, multiply both sides by z₁⁻¹: z₂=0. Similarly if z₂≠0 then z₁=0. Conclusion: at least one of z₁ or z₂ must equal 0. Answer: z₁=0 or z₂=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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