The product of two complex numbers x + it and x' + iy' is zero. Which of the following statements is most appropriate?
- One of the complex numbers is zero
- Both complex numbers must be zero
- The real parts of both are zero
- None of these
Explanation
Given the product of two complex numbers (x + iy) and (x' + iy') is zero:
(x + iy)(x' + iy') = 0
This implies either (x + iy) = 0 or (x' + iy') = 0.
Therefore, at least one of the complex numbers must be zero.
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