CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 11. Complex Numbers

Guided Practice

1. Simplify the following complex number.
   i^2013


2. Plot the following complex number on the complex coordinate plane and determine its absolute value.
   − 12 + 5 i


3. Fora= 3 + 4 i,b= 1 − 2 icompute the sum, difference and product ofaandb.
   Answers:


4. When simplifying complex numbers,ishould not have a power greater than 1. The powers ofirepeat in a four
   part cycle:

i^5 =i=√− 1

i^6 =i^2 =− 1

i^7 =i^3 =−√− 1 =−i

i^8 =i^4 = 1

Therefore, you just need to determine where 2013 is in the cycle. To do this, determine the remainder when you
divide 2013 by 4. The remainder is 1 soi^2013 =i.
2.

The sides of the right triangle are 5 and 12, which you should recognize as a Pythagorean triple with a
hypotenuse of 13. |− 12 + 5 i|=13.
3.

a+b= ( 3 + 4 i)+( 1 − 2 i) = 4 − 2 i

a−b= ( 3 + 4 i)−( 1 − 2 i) = 2 + 6 i

a·b= ( 3 + 4 i)·( 1 − 2 i) = 3 − 6 i+ 4 i+ 8 = 11 − 2 i