e^(ix)=cos(x)+isin(x). Let x=pi, therefor e^(i*pi)=cos(pi)+isin(pi) and as cos(pi)=-1 and sin(pi)=0, cos(pi)+isin(pi)=-1, so e^(i*pi)=-1. Maths!
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Audial
e^(ix)=cos(x)+isin(x). Let x=pi, therefor e^(i*pi)=cos(pi)+isin(pi) and as cos(pi)=-1 and sin(pi)=0, cos(pi)+isin(pi)=-1, so e^(i*pi)=-1. Maths!