### Video Transcript

What is the conjugate of the complex number four plus three 𝑖?

We need to recall the definition of the conjugate of a complex number. Suppose we have the complex number 𝑧 which is equal to 𝑎 plus 𝑏𝑖, its conjugate which is denoted by 𝑧 star is the complex number 𝑎 minus 𝑏𝑖.

The difference between a complex number and its conjugate is that the sign of the imaginary part has changed. So to find the conjugate of the complex number four plus three 𝑖, we just need to change the sign of the imaginary part. Positive three 𝑖 becomes negative three 𝑖.

The conjugate of the complex number four plus three 𝑖 is four minus three 𝑖.