What is the complex conjugate of #3i+4#?

2 Answers
Apr 22, 2015

If #z=4+3i# then #bar z = 4-3i#

A conjugate of a complex number is a number with the same real part and an oposite imaginary part.

In the example :
#re(z) = 4# and #im(z)=3i#
So the conjugate has:
#re(bar z) = 4# and #im(bar z)=-3i#
So #bar z = 4-3i#

Note to a question : It is more usual to start a complex number with the real part so it would rather be written as #4+3i# not as #3i+4#

Dec 8, 2015

Answer:

#4-3i#

Explanation:

To find a complex conjugate, simply change the sign of the imaginary part (the part with the #i#). This means that it either goes from positive to negative or from negative to positive.

As a general rule, the complex conjugate of #a+bi# is #a-bi#.

Notice that #3i+4=4+3i#, which is the generally accepted order for writing terms in a complex number.

Therefore, the complex conjugate of #4+3i# is #4-3i#.