What is the conjugate of minus the square root of minus #5# ?

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Answer 1 · 2017-09-07T18:56:43

#bar(-sqrt(-5)) = bar(-isqrt(5)) = isqrt(5) = sqrt(-5)#

If I interpret the question correctly, we want to find the complex conjugate of:

#-sqrt(-5)#

Note that if #n < 0# then:

#sqrt(n) = isqrt(-n)#

where #i# is the imaginary unit, satisfying #i^2=-1#

So:

#-sqrt(-5) = -isqrt(5)#

The complex conjugate of a number in the form #a+ib# where #a, b# are real is #a-ib#

So the complex conjugate of #-isqrt(5)# is #isqrt(5) = sqrt(-5)#.

A common notation for complex conjugate is a bar placed above the expression. So we can write:

#bar(-sqrt(-5)) = bar(-isqrt(5)) = isqrt(5) = sqrt(-5)#