Write an example of a complex number that is equal to its conjugate.
I understand it now!
a+bi=a-bi
so B has to equal zero
Your question makes no sense
If a+bi is your complex number, then its conjugate is a - bi,
but they are NOT equal.
However, if you want to trivialize it ....
the conjugate of a + 0i is a - 0i, and they would be equal since a = a
A complex number that is equal to its conjugate is a number of the form a + bi, where a and b are real numbers, and i is the imaginary unit.
To find such a complex number, suppose we have a complex number z = a + bi that is equal to its conjugate, denoted as z*.
The conjugate of z, denoted as z*, is obtained by changing the sign of the imaginary part. In other words, if z = a + bi, then z* = a - bi.
Let's equate z and its conjugate z*:
a + bi = a - bi
To solve this equation, we can separate the real and imaginary parts:
a = a
bi = -bi
From the second equation, we observe that the imaginary part of z is equal to the negative of itself, which means it must be zero.
Therefore, b = -b implies b = 0.
We are left with the real part equation a = a, which holds true for any real number a.
So, the complex number z = a + bi that is equal to its conjugate z* is simply any real number a, as the imaginary part is zero.
For example:
z = 5 + 0i, or simply z = 5
To find an example of a complex number that is equal to its conjugate, we need to recall the definition of a conjugate. The conjugate of a complex number is obtained by changing the sign of its imaginary part.
Let's consider a complex number in the form a + bi, where "a" represents the real part and "b" represents the imaginary part.
To satisfy the condition that the complex number is equal to its conjugate, we need its imaginary part to be zero. This implies that b = 0.
Therefore, the complex number a + 0i simplifies to just a, which means any real number will be equal to its conjugate.
For example, let's take a = 5. The complex number 5 + 0i is equal to its conjugate, which is simply 5.
So, in this case, the complex number that is equal to its conjugate is 5.