The conversation between human and AI assistant.
If we can invent a number [math]i[/math] so that [math]i^2=-1[/math], why can't we have a number a so that [math]\sin a=2[/math]?
Can you explain to me why we can't have a number [math]a[/math] so that [math]\sin a=2[/math]?
Actually, the sine function outputs values between -1 and 1, so it's not possible for [math]\sin a[/math] to equal 2. This is in contrast to the imaginary unit [math]i[/math], which is a valid concept in mathematics because it satisfies the equation [math]i^2=-1[/math].