# Discrete Math

**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 2*θ *+ *i *sin 2*θ*,where *i *∈
**C **and *i*2 _ −1.

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

## Tutor Answer

**Quality**

**Communication**

**On Time**

**Value**

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors