What is the complex conjugate of #10+6i#?

1 Answer
Nov 21, 2015

Answer:

#10-6i#

Explanation:

The conjugate of #a+b# is #a-b#. Example: the conjugate of #3x+6# is #3x-6#.

The complex conjugate is the exact same, except it includes #i# (the square root of #-1#). The conjugate of #a+bi# is #a-bi#. Therefore, the complex conjugate of #10+6i# is #10-6i#.

Conjugates, especially complex conjugates, can prove very useful. For example, if #10+6i# were the denominator of a fraction, you could multiply it by #10-6i# to get #100-6i^2=106#. Complex conjugates are a useful way to clear out the complex #i# from a denominator or other inopportune place.