Below is a set of six questions that were included in my assignment. I think I have a pretty good understanding but I am not real sure I am doing the long division ones the right way. If someone could check my work and provide feedback for anything that I am not doing correctly, I would really appreciate it. Thank you in advance for your time.

**1.**** Give examples for a Real number and a Complex number.**

**Real numbers**

natural numbers (1, 2, 3, 4, 5, etc.)

whole numbers (0, 1, 2, 3, 4, etc.)

integers (…-5, -4, -3, -2, -1, 0, 1, 2, etc.)

decimal numbers (0.1, 0.2, 0.3, 0.4, etc.)

rational numbers (7/4, 50/100, ½, etc.)

irrational numbers (1/3, 10/11, 3/13, 22/7 or 3.14, etc.)

**Complex numbers**

5*i*

22*i*

17*i*

5*i*

4*i*

9*i*

3i

**2. Simplify the following expressions**

**(a). (x3)2**

** X6**

**(b). y5.y8**

**y13**

**(c). (x3y5)/y2**

**x3y3**

**(d). 27a^4b^8c^-3** ** ----------------** ** 3a^-3b^2** **9a^7b^6 ** ** --------- ** ** c3** **(e). (x+4)(x+6)** **x2 + 10x + 24** **(f). (x2-3)(x +7)** **x3 + 7x2 – 3x – 21** **3. Simplify (x2 +8x +15)/(x2-25)** **4. Simplify** **a^3 + 9a^2 + 27a + 27 ** ** ----------------------** ** a + 3** ** (a + 3)(a + 3)(a + 3)** ** -------------------- ** ** a + 3** **5. Divide x^4 + 3x^3 + x^2 + 1 by (x-1)** **6. Divide ****6y^3 + 2 by (y + 1)**