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We know that if we have two complex numbers in polar format (i.e., magnitude and exponential), that for two complex vectors

z1 = A*exp(iB)

z2 = C*exp(iD)

If z1 and z2 are equal, then A = C and B = D. However, this is assuming these values are all real. What if they are complex? I.e. can we say if we have two complex numbers

z3 = (a+ib)*exp(c+id)

z4 = (e+if)*exp(g+ih)

If z3 and z4 are equal, can we say that (a+ib) = (e+if) and (c+id) = (g+ih)?

Thanks

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# Equating Complex Numbers

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