the complex expression eylength + iθ when y-length is 0


In the diagram, if θ were to equal π  (180°), then the
y-length of B2A2, relative to O, is 0, and the value of
each expression is -1, the four expressions adding up to -4.


eylength + iθ = eylength (Cosθ + iSinθ) = 1 (-1 + 0)

e = -1


eylength - iθ = eylength (Cosθ - iSinθ) = 1 (-1 - 0)

e-iπ = -1


e-ylength + iθ = e-ylength (Cosθ + iSinθ) = 1 (-1 + 0)

e = -1


e-ylength - iθ = e-ylength (Cosθ - iSinθ) = 1 (-1 - 0)

e-iπ = -1