- #1
coreanphysicsstudent
- 3
- 0
- Homework Statement
- solve i^2/3 using complex number.
- Relevant Equations
- below is my solution.
i^2/3=e^(2/3(lni)), ※(lni = i(pi/2+-2npi))
=e^2/3(i(pi/2+-2npi))=e^i(pi/3+-4/3npi)
※e^i(+-4/3npi)=+-1 (is tha correct?) .....(*)
e^ipi/3 = (1/2 + root3/2i)..........(**)
(**)(*) =e^i(pi/3+-4/3npi)= i^2/3 (using property of exponents)
So, my answer is +-(1/2+root3/2i)
but the real answer is −1, (1±i√3)/2
What's wrong with my solution?
please help me through.
What's wrong with my solution?
please help me through.