Courtney and Katie’s Adventure Through the Wild World of Complex Numbers By: Courtney and Katie
One day there were two best animal friends named Courtney and Katie. They were walking through the jungle when they came about a smart jungle man named Hannah. He helped them through the jungle while teaching them about complex numbers.
Hannah taught them that every complex number is written in the form a + bi . a+bi a+bi
I still don’t understand it. What does a+bi stand for?
Well, great question Katie, in the formula, a+bi, a stands for the real number while bi represents the imaginary unit.
Tell me more please. Well, Complex numbers can be added, subtracted, multiplied, and divided using the equation
So, when adding, for example, (2+3i)+(4+5i) First you add the real parts together where 2+4=6. Then, add the imaginary parts together, where 3i+5i= 8i. Then the solution is...? 6+8i
Well, you see, Courtney... Let’s look at a new example, but this time, for multiplication. (2+i)(3-2i)
Multiplying complex numbers works like multiplying two binomials by using the FOIL method. After you FOIL the equation, then you combine the real parts and the imaginary parts. After solving this equation, the solution is... Guest Starring: Kaa as Erik
A division problem is usually given in fraction form. To solve a division problem, we will need to know the conjugate of the denominator. The conjugate is simply the same numbers of the complex number but with a different sign between them. For example, the conjugate of 3-4i is 3+4i . The terms are the same but with a different sign. Notice what will happen if you multiply the original number and its conjugate together...
In order to explain to you, Courtney, the steps needed to complete a division problem involving complex numbers, lets simplify the equation .
Multiply both the numerator and the denominator by the conjugate of the denominator. Simplify the terms.