For (i), after using De Moivre's Theorem we obtain:
-2
U cannot use LOGS
Show meConstruct vectors A, B, B*, AB* and AB*-1. We immediately observe two congruent triangles, where matching sides include |A-B| and |AB*-1| and hence the result.
Yes i know, just a trick question...-2
this is a 2U question.
no it isn'tYes i know, just a trick question...
lol this question nearly made the BOS Trials.The Fibonacci sequence is a sequence of numbers whereby each term of the sequence is the sum of the previous two terms, the sequence starts off with two terms
1, 1
Then it goes on following the Fibonacci rule:
1, 1, 2, 3, 5, 8, 13, 21 ...
Notice how each term is the sum of the previous 2 terms.
The proof by induction is quite easy, do you mean the derivation of the result?lol this question nearly made the BOS Trials.
The induction method, then I extended the question to a limit problem.The proof by induction is quite easy, do you mean the derivation of the result?
This is going beyond syllabus now
(Do not worry about whether it is actually possible to take exponentials of complex numbers)
Something interesting to note that the complex exponential function is peroidic with period 2pi i
(Do not worry about whether it is actually possible to take exponentials of complex numbers)
Technically, the logarithm MULTIfunction unless we choose a branch.Something interesting to note that the complex exponential function is peroidic with period 2pi i
It does make the complex logarithm function a bit complicated though.
I suppose, but I think it is somewhat limiting to only think of it as a function...much of complex analysis is based on the theory of multifunctions. Anyway, very off-topic.Well, usually one chooses a branch cut according to what needs to be evaluated...