Subjects algebra

Imaginary Unit 6391Cd

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Imaginary Unit 6391Cd


1. The problem asks what happens if $i = 1$. 2. Normally, $i$ is defined as the imaginary unit where $i = \sqrt{-1}$ and $i^2 = -1$. 3. If we set $i = 1$, then $i^2 = 1^2 = 1$ instead of $-1$. 4. This means the fundamental property of the imaginary unit is lost, and $i$ behaves like a real number. 5. Complex numbers rely on $i^2 = -1$ to represent numbers beyond the real line. 6. So, setting $i = 1$ means we are no longer working with complex numbers but just real numbers. 7. In conclusion, $i = 1$ changes the nature of the number system and invalidates the concept of imaginary numbers.