What is conjugate of #i#?

1 Answer
Oct 18, 2015

Answer:

The conjugate of #i# is #-i#

Explanation:

If #a, b in RR# then the conjugate of #a+ib# is #a-ib#.

When you have a polynomial equation with Real coefficients, any Complex non-Real roots that it has will occur in conjugate pairs.

For example, #x^2 + x + 1 = 0# has two roots: #-1/2+sqrt(3)/2i# and #-1/2-sqrt(3)/2i#.

#x^2+1=0# has two roots #i# and #-i#.

You could say that from the perspective of #RR#, the numbers #i# and #-i# are indistinguishable. When we extend #RR# to make #CC# we pick one of the square roots of #-1# and call it #i#. Then the other is #-i#, but they could just as easily be the other way around.