Evaluate the complex number into real and imaginary parts √i√i.
Solution
From indices we know that √i=i12
i12=[cosπ2+isinπ2]12=cosπ4+isinπ4=1√2+i1√2.
Therefore,
=e−π4√2.eiπ4√2=e−π4√2.[cosπ4√2+isinπ4√2]
Therefore, the
Real part =e−π4√2cosπ4√2
Imaginary part =e−π4√2sinπ4√2
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