Good work. I just have a small elaboration. When the Cauchy Riemann Equations are satisfied alone does not necessarily mean the function is Analytic. The partial derivatives should also be continuous. For this example, the partial derivatives are continuous hence the function is analytic. To summarize my point let me state a theorem. A complex valued function is Analytic/Holomorphic if and only if the Cauchy Riemann Equations are satisfied and the partial derivatives are continuous.
Thank you for your thoughtful comment and elaboration! You're absolutely right-satisfying the Cauchy-Riemann equations alone doesn't guarantee analyticity without the continuity of the partial derivatives. Your explanation is a great addition to the discussion, and I truly appreciate you taking the time to share it. Insights like these make the learning experience richer for everyone. It’s always great to have such engaging contributions on the channel!
Good work. I just have a small elaboration. When the Cauchy Riemann Equations are satisfied alone does not necessarily mean the function is Analytic. The partial derivatives should also be continuous. For this example, the partial derivatives are continuous hence the function is analytic. To summarize my point let me state a theorem. A complex valued function is Analytic/Holomorphic if and only if the Cauchy Riemann Equations are satisfied and the partial derivatives are continuous.
Thank you for your thoughtful comment and elaboration! You're absolutely right-satisfying the Cauchy-Riemann equations alone doesn't guarantee analyticity without the continuity of the partial derivatives. Your explanation is a great addition to the discussion, and I truly appreciate you taking the time to share it. Insights like these make the learning experience richer for everyone.
It’s always great to have such engaging contributions on the channel!
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Very easy to comprehend ❤more wisdom
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Very explanatory to the core ❤
Awesome
Thanks for the review 👍🏿
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Nice one ❤️✅
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Thanks 🔥😊
Sir calculus for a reason 🎉👏❤️
Thank you😊
Thanks 🙏
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Thank you ❤
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Thank you so much ❤
You're welcome 😊
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Thanks so much
The thermodynamics really helped me in the exam🥹🫡
You're welcome!
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Do you by any chance have a Whatsapp group that you create awareness when you are having a real class boss@@FURTHERACADEMY