TI-92 square root bug

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TI-92 square root bug

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

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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