SOLUTION: Divide: (4 + 2i)/ (4 – 2i) I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. T

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Divide: (4 + 2i)/ (4 – 2i) I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. T      Log On


   

Question 213435: Divide: (4 + 2i)/ (4 – 2i)
I need help with this . Can someone please explain what to do for me using this example. I need to know the steps as well as how you got the answer. Thankyou for you time. Your are appreshated.
Found 2 solutions by stanbon, drj:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
You need to remember that (a-b)(a+b) = a^2-b^2
---------------
Divide: (4 + 2i)/ (4 – 2i)
------------------------
Multiply numerator and denominator by 4+2i to get:
(4+2i)^2/(4^2-(2i)^2)
----
Simplify:
[16 + 16i + (2i)^2]/ [16+4]
---
[16 +16i -4]/20
---
[12+16i]/20
---
[4(3+4i)]/20
---
(3+4i)/5
===============
Cheers,
Stan H.

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Divide: %284%2B2i%29%2F+%284-2i%29

Step 1. Multiply by 1 where %284%2B2i%29%2F%284%2B2i%29=1 so that the denominator is not complex.

Step 2. This will result in the following steps

%284%2B2i%29%2F%284-2i%29=%28%284%2B2i%29%2F%284-2i%29%29%2A%284%2B2i%29%2F%284%2B2i%29

Now the denominator will be

%284-2i%29%284%2B2i%29=%284%29%284%29-%284%29%282i%29%2B%282i%29%284%29-%282i%29%282i%29

%284-2i%29%284%2B2i%29=16-%284%29i%5E2=16-4%2A%28-1%29%29=20 where i=sqrt%28-1%29

%284%2B2i%29%2F%284-2i%29=%284%2B2i%29%2A%284%2B2i%29%2F20

Now the numerator will be

%284+%2B+2i%29%5E2=16%2B2i%2B2i%2B4i%5E2=16-4%2B4i=12%2B4i

%284%2B2i%29%2F%284-2i%29=%2812%2B4i%29%2F20=%283%2Bi%29%2F5


I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J