Discrete Math

Nov 24th, 2013
Anonymous
Category:
Art Design
Price: $40 USD

Question description

I need 12 problems done for a discrete math class.....the two below are examples....there are over 30 problems to choose from (you can pick)


Example 1

12. a) Prove that (cos θ + i sin θ)2 _ cos 2θ + i sin 2θ,where i C and i2 _ −1.

b) Using induction, prove that for all n Z+,(cos θ + i sin θ)n _ cos + i sin nθ.

(This result is known as DeMoivre’s Theorem.)

c) Verify that 1 + i _√2(cos 45◦ + i sin 45◦), and compute(1 + i)100.


Example 2

2. For each of the following functions f : Z→Z, determine

whether the function is one-to-one and whether it is onto. If the

function is not onto, determine the range f (Z).

a) f (x) x + 7 b) f (x) 2x − 3

c) f (x) −x + 5 d) f (x) x2

e) f (x) x2 + x f ) f (x) x3






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