Question

Prove that: √i +√1/i=√2​

Answer 1

This is nominally the sum of conjugates so should be real, indicating some problems with the other answers.

In fact, with complex numbers it’s best to treat the non-integer powers and square roots as multivalued. So this will have four values, from the two possible values of each square root. Two of them will be the sum of conjugates, so real.

i is 90∘ so it has square roots at 45∘ and 45∘+180∘.

i√=±12–√(1+i)

Similarly,

−i−−√=±12–√(1−i)

i√+−i−−√=±12–√(1+i)±12–√(1−i)

i√+−i−−√=−2–√,−2–√i,2–√, or 2–√i

mark as brainliest answer please