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 - 4i) + (-5 - 2i)

(b) (6i - 4)(3i + 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 - 4i) + (-5 - 2i)

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

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

Again, this is simple gr.9 mechanics with a hint of Gr.11. Multiply the 2 binomials, substitute i² 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.

i³ = -i

This is because...

i^3 = i x i x i

Then we simplify it even further by substituting all the i² with -1 because i² = -1. Simplify it even more and we're done!

Problem 3 of 3

(a) If , then evaluate x⁴.

(b) Solve:

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

Solution