I apologize for the confusion, but there is still an error in the reasoning.. Let's go through it step by step:

The imaginary number (i) raised to the 4th power: i^4 = (i * i * i * i) = 1.
The imaginary number (i) raised to the 8th power: i^8 = (i * i * i * i * i * i * i * i) = 1.
Here, both i^4 and i^8 equal 1.
Taking the square root of both sides:
√(i^4) = √(i^8)
√1 = √1
1 = 1
Based on this step, we can conclude that 1 equals 1, not -1.

The error lies in the statement that the square root of i^4 equals the imaginary number squared, which is -1. In fact, the square root of a positive number like 1 has two possible solutions: +1 and -1. Both values satisfy the equation when squared, resulting in 1. Similarly, the square root of i^8 is also 1.

In your argument, you have incorrectly stated that the square root of i^8 equals the imaginary number raised to the 4th power, which is 1. However, the square root of i^8 is actually 1 itself, not i^4.

Again, it's important to note that the equation -1 = 1 is not mathematically accurate. The steps in your argument contain errors or misinterpretations of mathematical principles. It's crucial to follow valid mathematical reasoning and principles to avoid reaching incorrect or contradictory conclusions.

On 7/18/2023 12:57 PM, patdolan wrote:
>
>
> I apologize for the confusion, but there is still an error in the reasoning. Let's go through it step by step:
>
> The imaginary number (i) raised to the 4th power: i^4 = (i * i * i * i) = 1.
> The imaginary number (i) raised to the 8th power: i^8 = (i * i * i * i * i * i * i * i) = 1.
> Here, both i^4 and i^8 equal 1.
> Taking the square root of both sides:
> √(i^4) = √(i^8)
> √1 = √1
> 1 = 1
> Based on this step, we can conclude that 1 equals 1, not -1.
>
> The error lies in the statement that the square root of i^4 equals the imaginary number squared, which is -1. In fact, the square root of a positive number like 1 has two possible solutions: +1 and -1. Both values satisfy the equation when squared, resulting in 1. Similarly, the square root of i^8 is also 1.
>
> In your argument, you have incorrectly stated that the square root of i^8 equals the imaginary number raised to the 4th power, which is 1. However, the square root of i^8 is actually 1 itself, not i^4.
>
> Again, it's important to note that the equation -1 = 1 is not mathematically accurate. The steps in your argument contain errors or misinterpretations of mathematical principles. It's crucial to follow valid mathematical reasoning and principles to avoid reaching incorrect or contradictory conclusions.

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