Complex Number Property | MCQs
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A. Both complex numbers must be zero
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B. One of the complex numbers is zero
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C. The real parts of both are zero
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D. 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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A. arg (Z1 Z2) = arg Z1 + arg Z2
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B. None of these
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C. arg (Z1 Z2) = arg Z1 - arg Z2
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D. arg (Z1 Z2) = arg Z1 . arg Z2
Explanation
The argument of the product of two complex numbers is the sum of their arguments.
This property comes from the multiplication of complex numbers in polar form.
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