Is the derivative of y = x^i equal to ix^{i-1} and is y always real?

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SUMMARY

The derivative of the function y = x^i, where x is a real number and i is the imaginary unit, is correctly expressed as y' = ix^{i-1}. However, y is not always real; when expressed in exponential form, y reveals its complex nature. The discussion confirms that while the derivative calculation is accurate, the assertion that y must be real is incorrect.

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MHD93
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Hello guys

Let
[tex]y = x^i[/tex]
x is real, i imaginary, then is it right to say:

[tex]y' = ix^{i-1}[/tex]

and must y be real?
 
Last edited:
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The derivative is correct. But why would you claim y is real? If you write it in terms of the exponential and expand, you see that y is complex.
 

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