Simplify without the use of calculator [cos (pi/7) – i sin (pi/7)]^3 / [ cos (pi/7) + i sin (pi/7)]^4 How can I solve this?
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Hello geton, From your posts elsewhere I think you know the form of a complex number. In this case you wont need the R. Once you have them in that form it should be easy to simplify.
Originally Posted by a tutor Hello geton, From your posts elsewhere I think you know the form of a complex number. In this case you wont need the R. Once you have them in that form it should be easy to simplify. I know z₁ = r(cosѲ + i sinѲ) & z₂ = r(cosѲ - i sinѲ). But how can I solve by this?
Recall this basic principle: . Thus:
Originally Posted by Plato Recall this basic principle: . Thus: But what about denominator. I didn't understand properly. Can you explain for me?
Originally Posted by geton But what about denominator. I didn't understand properly. Can you explain for me? Using deMoivre's Theorem: Then you just divide numerator by denominator using the usual rule for division of complex numbers expressed in polar form to get:
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