Consider DeMoivre's theorem in exponential form:
If $z=re^{i\theta}$ z=re^{i\theta} then $z^{-n}=r^{-n}e^{-in\theta}$ z^{-n}=r^{-n}e^{-in\theta} for $n = 1,2,3,\ldots$ n = 1,2,3,\ldots.
If we let n=0 which of the following statements will be true?

Question

Consider DeMoivre's theorem in exponential form: If   z=re^{i	heta}  then   z^{-n}=r^{-n}e^{-in	heta}  for   n = 1,2,3,\ldots . If we let   n=0  which of the following statements will be true?

Answer

For   z=re^{i	heta}  when   n=0  we have   z^0 = r^0e^{0i	heta}=1+i .

Answer

We cannot use DeMoivre's theorem for   n=0  as it only applies when   n  is a positive or negative integer.

Answer

For   z=re^{i	heta}  when   n=0  we have   z^0 = r^0e^{0i	heta}=0 .

Answer

For   z=re^{i	heta}  when   n=0  we have   z^0 = r^0e^{0i	heta}=1 .

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Consider DeMoivre's theorem in exponential form: If z=re^{i\theta} then z^{...

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