Learning Objectives

# Problem 1 of 3

The point P lies on the y-axis, while points A and B are (-9, 0) and (5, 0) respectively. If PA + PB is 28 units long, determine the coordinates of P.

**Solution**

# Problem 2 of 3

*Evaluate each of the following:*

(a) (3 - 4*i*) + (-5 - 2*i*)

(b) (6*i* - 4)(3*i* + 2)

(c) (1 + *i*)^{3}

**Solution**

***Before we start solving these questions, we must understand that *i* = the root of -1. This also means that i^2 = -1.

***It's best if we treat *i* as just a variable and *then* we substitute the value of *i*.

**(a) (3 - 4***i*) + (-5 - 2*i*)

This is simple gr.9 mechanics. Just combine the like terms and you're done!

**(b) (6***i* - 4)(3*i* + 2)

Again, this is simple gr.9 mechanics with a hint of Gr.11. Multiply the 2 binomials, substitute *i*^{2} with -1, simplify, and you're done!

**(c) (1 + ***i*)^{3}

NOW things get *complexed* (no pun intended). This is a true test to see if you understand the "i" symbol. First off, you multiply the binomials to get a trinomial. Next you multiply the trinomial with the binomial to get a 4-degreed polynomial. This is where the concept of the "i" is put to the test.

*i*^{3} = -*i*

This is because...

i^3 = i x i x i

Then we simplify it even further by substituting all the *i*^{2} with -1 because *i*^{2} = -1. Simplify it even more and we're done!

# Problem 3 of 3

(a) If , then evaluate x^{4}.

(b) Solve:

(c) Solve and express your answer using interval notation:

**Solution**

**Mr. K. says:** *You didn't log in to the wiki using your name. You can't get credit for doing any work on the wiki unless you do. Also, you CANNOT "claim" a question just by saying "I want this one." You can only "claim" a question by solving. This question is still open for anyone to claim. Whoever first starts to solve this problem can delete this comment.*

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