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anonymous
 3 years ago
simplify the expression
23i/1+5i
anonymous
 3 years ago
simplify the expression 23i/1+5i

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mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1356499621903:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0When i punched it into a calculator, it told me it was 2+2i

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0in order to simplify this type of equations rationalizing the denominator allows to get a simple equation

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1Here 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
 3 years ago
Best ResponseYou've already chosen the best response.1The 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.

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1So by multiplying your original fraction by (1  5i)/(1  5i) you are not changing the value, only the form.

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1356499890726:dw

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1356500006418:dw

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1356500358308:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so the answer is 1/2  1/2i

mathstudent55
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1356500446208:dw
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