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Calculate 1/(1+2i)+1/(1-2i)

Solution

We\'ll multiply both fractions by the value of the least common denominator:

LCD = (1 + 2i)(1 - 2i)

LCD = 1^2 - 4i^2, where i^2 = -1

LCD = 1 + 4 = 5

1/(1+2i)+1/(1-2i) = (1 - 2i + 1 + 2i)/5

We\'ll combine and eliminate like terms:

1/(1+2i)+1/(1-2i) = 2/5

The value of the addition of the given fractions is: 1/(1+2i)+1/(1-2i) = 2/5.