When I type in the identity eπ√−1 on my phone calculator (LG phone running Android), I get the correct result of −1
However, when I simply type √−1, it returns an error.
Why can the calculator do eπ√−1, but not do √−1 if √−1 is a direct part of eπ√−1?
Answer
eπ√−1=cosπ+√−1sinπ=−1+0=−1 which is a real number
BUT
√−1=i is a complex number with a zero real part and a non-zero imaginary part.
Computation of complex numbers is possible in any calculator but showing the results containing imaginary numbers is not possible except in certain high-grade calculators.
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