Q The principal of ii is equal to - a e - Maths - Complex Numbers and Quadratic Equations

Question

Q The principal of i i is equal to -
a   e                
                 
          b   e - π / 2  
                 
            c   e - 3 π / 2
                 
        d   n o n e   o f   t h
e s e

Explain stepwise with formulas if any

Neha Sethi · Accepted Answer

Dear student
Sometimes according to the need of the answer, we make the requiredsubstitutions
If we will put x=0 in, eix=cosx+isinx⇒ei0=cos0+isin0⇒e0=1+0⇒1=1    as e0=1but this will not lead to any conclusion
Again if we put x=π3 in, eix=cosx+isinx⇒ eiπ3=cosπ3+isinπ3⇒eiπ3=12+i32Again  this will not lead to any conclusion
But if we put x=π2 in, eix=cosx+isinx⇒ eiπ2=cosπ2+isinπ2⇒eiπ2=0+1i⇒i=eiπ2This way we are able to proceed and will get the desried result
Regards

Q. The principal of i i is equal to - a . e b . e - π / 2 c . e - 3 π / 2 d . n o n e o f t h e s e Explain stepwise with formulas if any.

Q. The principal of $i^{i}$ is equal to -
$a . e b . e^{- π / 2} c . e^{- 3 π / 2} d . n o n e o f t h e s e$

Explain stepwise with formulas if any.