Re: TI-92 square root bug

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Re: TI-92 square root bug

Andre Silva schrieb:
>
> I've found this weird bug in my TI-92 when dealing with the squareroot
> of complex numbers. When the imaginary part of a complex number has a
> low exponential the square root of that number is 0.For example:
> The square root that the TI-92 calculates of the numbers below are:
> SQRT(50 + i1)=7.07142+.070707i
> SQRT(50 + i1E-5)=7.07107++7.07107E-7i
> SQRT(50 + i1E-10)=0   (!!!!!!!!!THE BUG!!!!!!!)
> SQRT(50 + i1E-15)=7.07107

Not on the 92+                  A.K.
>
> More details about the bug
>
>        I found that the square root bug calculating complex numbers
> occurs only when the the difference of digits between the real part and
> the imaginary part is at least 7, i.e.
> Number of digits of real part - number of digits of imaginary part = 7
>
> For example, the following number are represented by letters, in wich a
> letter is any number between 0 and 9.
>
> abcd= 4 digits
> ab= 2 digits
> a= 1 digit
>
> now let's consider this:
>
> 0.a= 0 digits
> 0.ab = -1 digit
> 0.abcd= -3 digits
>
> and so on...
>
> So if we try to calculate de square root of 123456789 + i*64 it will
> present the zero result, because 9 digits - 2 digits= 7 digits.
>
>  The same would happen if the number was 1234567 + i*0.02, since now the
> number of digits are 7 - (-1) = 8 (remember, the difference must be at
> least 7). Of course that if the imaginary part is very small, then the
> TI-92 will consider it 0, giving only the result of the real part.
> If, instead of directly calculating the square root of, for example,
> 50+i5E-7, we calculate (50+i5E-7)^(1/2), the result will be the same, 0,
> even calculating the square root with another method. But if we
> calculate (50+i5E-7)^.5 the result will be different of 0!!!!!!!!!!!!
>
> But the answer, it still won't be the correct one.
>
> Note: Calculating the powers of complex numbers, if the power is <1
> then it will give erronoeous results in the degree mode, but will give
> the correct answer in the radian mode. Just like making calculations
> with polar complex numbers in the degree and radian mode.
>
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