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15.10.2020 1 et. z

Solution z1z2 = (5− 2j)(2+4j) = 10+20j −4j − 8j2 Replacing j2 by −1 we obtain z1z2 = 10+16j −8(−1) = 18+16j In general we have the following result: www.mathcentre.ac.uk 7.2.1 c Pearson Education Ltd 2000 News, email and search are just the beginning. Discover more every day. Find your yodel. Deﬁnition. For z ∈ C we deﬁne cosz = 1 2 (eiz +e−iz); sinz = 1 2i (eiz −e−iz); coshz = 1 2 (ez +e−z); sinhz = 1 2 (ez −e−z).

Eisenstein integers O = Z[ω] (ω = e(1/3)) with small norm (the points). The points corresponding to prime elements p are filled in and circles with radii equal to

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Let x = e^z, so we have: x^2 + x + 1 = 0. This is now a regular quadratic (which cannot be factored) so we complete the square: x^2 + x = -1. x^2 + x + 1/4 = -3/4 (x + 1/2)^2 = -3/4. x + 1/2 = +/- sqrt(3)i/2.

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