Why do calculators give a math error for sqrt(-1 * 1)?

[SSan]

When I try to do :

sqrt(-1 * 1)

I come up with a Math Error or Infinity(varying on the caclulator used).

Explinations?

 

[BoulderHead]

The calculator is likely set for real mode. The calculation you're performing has i for an answer, and i is not a real number. Look for options with your calculator to give you a+bi output.

Good luck

 

[Zorodius]

Think about what the square root means. It's the answer to the question, "what do I have to multiply by itself to get to this number?" The square root of nine is the number that, when multiplied by itself, gives you nine - that number is three.

What about the square root of negative nine? Can you think of any number that, when multiplied by itself, gives you negative nine? Positive three times positive three is positive nine, that doesn't work. Negative three times negative three is still positive nine (remember, multiplying two negative numbers gives you a positive result.) There isn't any real number that you can multiply by itself and arrive at negative nine.

As a matter of fact, that's true for the square root of any negative number. Furthermore, it's true for any even root of any negative number. Your calculator is giving you an error because it's only designed or configured to display real numbers, and there aren't any real numbers that answer the question, "what is the square root of negative one?"

 

[Gokul43201]

This reminds me of the following :

1 = SQRT(1) = SQRT(-1*-1) = SQRT(-1)*SQRT(-1) = SQR(i) = -1

Kinda clever for a couple of seconds, until you look at the first step again.

 

[killerinstinct]

sqrt

sqrt(-1) = i
sqrt(-4) = 2 i
sqrt(-6) = 2.44948974 i

and so on...
Any calculator under TI-89 will give you an "nonreal ans" because they are not programmed to recongnized imaginary numbers unless otherwise told to.

 

[catch.yossarian]

Any calculator under TI-89 will give you an "nonreal ans" because they are not programmed to recongnized imaginary numbers unless otherwise told to.

I tried my TI-89 and it gives me an error when I try to do the Sqrt(-x); x being any numerical digit. Do you know of a way to remedy this, or is the TI-89 also a calculator which won't return i for an answer?

 

[master_coda]

I tried my TI-89 and it gives me an error when I try to do the Sqrt(-x); x being any numerical digit. Do you know of a way to remedy this, or is the TI-89 also a calculator which won't return i for an answer?

Your calculator should have a MODE button. If you press it a list of options should come up, and one of them should be "complex format". If it's set to "real" then complex numbers will not work.

 

[Euphoriet]

thats odd .. why do they set the option in the calculator to that if most people will use complex numbers such as i?