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a
e−π2
b
eπ2
c
eπ
d
e−π
answer is A.
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Detailed Solution
ii=[cos(π2+2rπ)+isin(π2+2rπ)]i,r=0,±1,±2 ..... [ei(π2+2rπ)]i=e−(π2+2rπ), r=0,±1,±2,.........We get ii=e−π2 when r=0 ALTERNATE: let ii=a+ib⇒ilogi=log(a+ib)⇒i.iπ2=log(a+ib) ∴a+ib=e−π2