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The number of complex number z such that (z-1) =(z-i) equal
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The number of complex number z such that (z-1) =(z-i) equal
Understanding the Equation
The equation given is (z - 1) = (z - i). To find the complex numbers z that satisfy this equation, we first simplify it.
Step 1: Simplifying the Equation
- Start by rewriting the equation:
(z - 1) - (z - i) = 0
- This simplifies to:
-1 + i = 0
- Rearranging gives us:
i - 1 = 0
Step 2: Analyzing the Result
The equation i - 1 = 0 indicates that the left side equals zero only when both components are equal. This means that:
- The real part must equal zero:
Re(z) = 1
- The imaginary part must equal zero:
Im(z) = i
However, since i is not zero, we can conclude this equation does not hold true.
Step 3: Conclusion
- Since the equation leads us to a contradiction, there are no complex numbers z that satisfy the equation (z - 1) = (z - i).
Final Statement
Thus, the number of complex solutions for the equation (z - 1) = (z - i) is zero, meaning there are no complex numbers that meet this criterion.
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The number of complex number z such that (z-1) =(z-i) equal
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The number of complex number z such that (z-1) =(z-i) equal
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