Question 25 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.
Q25. If , then the value of is,
Going by the definition of imaginary unit, and
From Euler’s formula, .
Based on the above, the right choice is : (a) i.e. if , then .
 GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf
 Imaginary unit
 Euler’s formula
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