Simplify Complex Fraction: 1/i + 1/(1+i) + 1/(1-i)
Published on August 4, 2024
Question
simplify it
Answer
To simplify the expression
, we’ll need to work with the imaginary unit
and manipulate these fractions. Here’s a step-by-step solution:
1. Rationalize the denominators:
-
For the first term, multiply the numerator and denominator by
: Since , we have: -
For the second term, multiply the numerator and denominator by the conjugate of the denominator,
: Simplifying, we get: -
For the third term, multiply the numerator and denominator by the conjugate of the denominator,
: Simplifying, we get:
2. Combine the terms:
Now our expression looks like this:
Combining the fractions, we get:
3. Simplify:
Notice that the
and
terms in the numerator cancel out:
This leaves us with:
Therefore, the simplified form of the expression is 1 - i.