Calculator gives the solution of "$10^2+(10i)^2$" as "$1.22464679914735\times10^{-14}i$" instead of zero. Why?

Question

Now solving on pen and paper as well as online calculators including wolfram alpha gives the result as 0 as expected. But using a calculator on android gives the solution as $1.22464679914735\times10^{-14}i$. I am attaching the picture. Can anyone explain what is going on? take a look

Edit: Thanks for the edit Chase

Answer 1

The number 1.22464679914735*10^(-14)i is so small it is basically zero. I have experienced this myself, and I was told that some calculators tend to display an extremely small number instead of zero. If you round 1.22464679914735*10^(-14)i you do get 0 as a result.

You can find an interesting article about this here (it is useful in your case even though it uses Excel as an example).

Answer 2

The calculator is nothing but a computer program. Some may be programmed to recognize the integer exponent. But others, like the one you used, probably used a general formula like $x^y=\exp (y\log x) $. This was performed using floating point arithmetic and errors are unavoidable since $\log10$ is irrational.