Rectangular form to exponentia

Yes if j= square root of -1

Usually, we say that i=square root of -1

Eular found that e^(it) = cos (t)+i sin(t) , which is the expand definition for e^x in complex domain.

e^(i * -pi/3 ) = cos ( -pi /3 )+i sin( -pi /3 ) = 1/2- i sqrt(3)/2

e^(it) = cos (t)+i sin(t) is called Eular Formula.

The proof is done by Taylor Expansion for e^x, cos(x) and sin(x).
You can find it in Wikipedia.

exp(ix) = cosx + isinx

exp(-iπ/3)

= cos(-π/3) + isin(-π/3)

= 1/2 - √3/2 i