If f (x) = x + 1/x, find f (1+3i)

f (x) = x + 1/x

f (1 + 3i), lets just sub x by 1 + 3i

f (1 + 3i) = 1 + 3i + 1 / (1 + 3i)

Doing the sum (1 + 3i) + 1 / (1 + 3i) we get ((1 + 3i) ² + 1) / (1 + 3i)

So:

f (1 + 3i) = (1 + 2.1.3i + 9i² + 1) / (1 + 3i)

f (1 + 3i) = (6i - 7) / (1 + 3i)

f (1 + 3i) = 11/10 + 27i/10

Step-by-step explanation:

f (1+3i) = (1+3i) + 1 / (1+3i)

=1+3i+1 / (1+3i)

= ((-8+6i) + 1) / (1+3i)

= (6i-7) / (1+3i)

=-25-15i

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