Inertia_Squared
Junior Member
- Joined
- May 24, 2019
- Messages
- 54
I've recently been on a blackpenredpen binge (great YouTube channel if you're interested), and in one of his videos he stated that [math]\sqrt{x} = -5[/math] has no solution for x, and even says there are no complex solutions. However if you let [math]x = 25i^4[/math] then as long as you acknowledge that [math]25 \neq 25i^4[/math] by assuming the RHS is always complex (i.e. that it cannot be further simplified, even though it obviously can) wouldn't that make it a valid solution?
[math]\text{Since } x = 25i^4, \text{then} \sqrt{x} = 5i^2 = -5[/math]
I know that this is a problem since sqrt{25} is not equal to -5, but if you treat 25 and 25i^4 as separate values I can't see how this causes any issues if you say it is a purely complex solution. I'm sure this is probably wrong, so if anyone knows a solid example that contradicts this assumption I would love to see it!
[math]\text{Since } x = 25i^4, \text{then} \sqrt{x} = 5i^2 = -5[/math]
I know that this is a problem since sqrt{25} is not equal to -5, but if you treat 25 and 25i^4 as separate values I can't see how this causes any issues if you say it is a purely complex solution. I'm sure this is probably wrong, so if anyone knows a solid example that contradicts this assumption I would love to see it!