anonymous
  • anonymous
simplify the expression 2-3i/1+5i
Mathematics
jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
|dw:1356499621903:dw|
anonymous
  • anonymous
When i punched it into a calculator, it told me it was 2+2i
anonymous
  • anonymous
in order to simplify this type of equations rationalizing the denominator allows to get a simple equation

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mathstudent55
  • mathstudent55
Here you need to get rid of i from the denominator. To do that, you need to multiply the denominator by its complex conjugate. The complex conjugate of a + bi is a - bi Since you are working with a fraction, whatever you multiply the denominator by, you must multiply the numerator by the same thing.
mathstudent55
  • mathstudent55
The complex conjugate of 1 + 5i is 1 - 5i (1 - 5i)/(1 - 5i) = 1 becasue when you divide a number by itself (except 0) you get 1.
anonymous
  • anonymous
okay so 1 -8i?
mathstudent55
  • mathstudent55
So by multiplying your original fraction by (1 - 5i)/(1 - 5i) you are not changing the value, only the form.
anonymous
  • anonymous
2+2i
mathstudent55
  • mathstudent55
|dw:1356499890726:dw|
mathstudent55
  • mathstudent55
|dw:1356500006418:dw|
mathstudent55
  • mathstudent55
|dw:1356500358308:dw|
anonymous
  • anonymous
so the answer is -1/2 - 1/2i
mathstudent55
  • mathstudent55
|dw:1356500446208:dw|
mathstudent55
  • mathstudent55
Correct
anonymous
  • anonymous
thank you
mathstudent55
  • mathstudent55
wlcm

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