i have 200 q's to do this summer. and im stuck on these 5. i have no one to consult with except you bright and intelligent people. please help...
#1. a) evaluate (1 + i)^2, where i = Squareroot(-1)
b) prove, by mathematical induction, that (1 + i)^(4n) = - 4^n, where n € N
c) hence or otherwise, find (1+ i)^32
#3. the variables x,y,z satisfy the simultaneous equations....
x + 2y + z = k
2x + y + 4z = 6
x - 4y + 5z = 9
where k is a constant.
a) (I) show that these equations do NOT have a unique solution.
(II) find the value of k for which the equations are consistent (that is, they can be solved).
b) for this value of k, find the general solutions of these equations
#5. solve the equation l e^(2x) - ( 1/ (x+2) ) l = 2
#4. the ratio of the fifth term to the twelfth term of a sequence in an arithmetic progression is 6 / 13. If each term of this sequence is positive, and the product of the first terms and the third term is 32, find the sum of the first 100 terms
2007-08-28
10:37:32
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4 answers
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asked by
Anonymous