# Is there any complex numer that is equal to its conjugate?

a+bi=a-bi?????

precalc 11th grade

a+bi=a-bi --->

2 bi = 0 --->

b = 0

So, the imaginary part has to be zero.

## To determine if there is any complex number that is equal to its conjugate, we can start by assuming that the complex number is of the form a + bi, where a and b are real numbers.

Now, the conjugate of a + bi is a - bi, where we change the sign of the imaginary part.

We can set up an equation to find if there exists a complex number that is equal to its conjugate:

a + bi = a - bi

Now, let's isolate the imaginary part on one side:

2bi = 0

To solve for b, we divide both sides of the equation by 2i:

b = 0

So, in order for a complex number to be equal to its conjugate, the imaginary part (b) must be equal to zero.

So, to answer your question, yes, there is a complex number that is equal to its conjugate, but it is only when the imaginary part is zero.