What is the complex conjugate of 3i+4?

2 Answers
Daniel L.
Apr 22, 2015

If z=4+3i then ¯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(¯z)=4 and im(¯z)=−3i
So ¯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

mason m
Dec 8, 2015

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.

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