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what is the value of iota(i) raise to the power iota(i)

what is the value of iota(i) raise to the power iota(i)

Grade:11

2 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

The value is e(pie/2) which if you expand gives the value -1

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

vikas askiitian expert
509 Points
13 years ago

z = ei@               (representation of complex number Z in ellulers form)

z1 = ii                  (given)

taking log both sides

logz1 = ilogi           .................1

 

now , logi = log(ei@)

              = log(eipi/2)

              = ipi/2

puting this value of logi in eq 1

 

logZ1 = i2(pi/2) = -pi/2                           (i2 = -1)

  Z1 = e(-pi/2)       , this is the required result

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