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(i) It can be proved that if z = a +ib, then . a e? = eeib = e(cos b + i sin b) (recall that e? is defined as the sum of
Posted: Thu May 12, 2022 1:36 pm
by answerhappygod
- I It Can Be Proved That If Z A Ib Then A E Eeib E Cos B I Sin B Recall That E Is Defined As The Sum Of 1 (44.36 KiB) Viewed 33 times
(i) It can be proved that if z = a +ib, then . a e? = eeib = e(cos b + i sin b) (recall that e? is defined as the sum of a certain series). In contrast to real ex- ponentiation, show that e? can be a negative real number. (ii) If w e?, where z is a complex number, then define log(w) = Z. In contrast to real logarithms, show that –1 has a logarithm; indeed, show that -1 has infinitely many logarithms.