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GATE-2012 ECE Q25 (math)

Posted By Krishna Sankar On October 9, 2012 @ 6:20 am In GATE | No Comments

Question 25 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper.

Q25. If , then the value of  is,

(a) 

(b) 

(c)

(d) 1

Solution

Going by the definition of imaginary unit [1] and

From Euler’s formula [2].

Putting ,

.

Substituting,

.

Based on the above, the right choice is :  (a) i.e.   if ,  then  .

 

References

[1] GATE Examination Question Papers [Previous Years] from Indian Institute of Technology, Madras http://gate.iitm.ac.in/gateqps/2012/ec.pdf [3]

[2] Imaginary unit [1]

[3] Euler’s formula [2]


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URLs in this post:

[1] imaginary unit: http://en.wikipedia.org/wiki/Imaginary_unit

[2] Euler’s formula: http://en.wikipedia.org/wiki/Euler%27s_formula

[3] http://gate.iitm.ac.in/gateqps/2012/ec.pdf: http://gate.iitm.ac.in/gateqps/2012/ec.pdf

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