Conjugate numbers

 Conjugate numbers

Conjugate numbers, also known as complex conjugates, are pairs of numbers with the same real part and opposite imaginary parts. In order to find the conjugate of a given number, you need to change the sign of its imaginary part. Let's go through the process step by step.

Step 1: Understanding Complex Numbers

A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' represents the imaginary unit (√(-1)). In this tutorial, we will focus on finding the conjugate of a complex number.

Step 2: Define the Given Complex Number

Let's consider a given complex number z = a + bi, where 'a' represents the real part and 'b' represents the imaginary part.

Step 3: Change the Sign of the Imaginary Part

To find the conjugate of z, we need to change the sign of the imaginary part (b). In other words, if b is positive, it becomes negative, and if b is negative, it becomes positive. The real part (a) remains unchanged.

Step 4: Write the Conjugate

The conjugate of z, denoted as z*, is obtained by changing the sign of the imaginary part of the given complex number z. So, the conjugate of z = a + bi is z* = a - bi.

Let's apply these steps to find the conjugate of the given numbers: 1, 2, 3, 4, 5.

For the number 1, the complex number can be represented as z₁ = 1 + 0i. Since the imaginary part is zero, the conjugate of z₁ will also be z₁* = 1 - 0i, which is simply 1.

For the number 2, the complex number can be represented as z₂ = 2 + 0i. Similar to the previous case, the conjugate of z₂ will be z₂* = 2 - 0i, which is 2.

For the number 3, the complex number can be represented as z₃ = 3 + 0i. The conjugate of z₃ will be z₃* = 3 - 0i, which simplifies to 3.

For the number 4, the complex number can be represented as z₄ = 4 + 0i. The conjugate of z₄ will be z₄* = 4 - 0i, which is 4.

For the number 5, the complex number can be represented as z₅ = 5 + 0i. The conjugate of z₅ will be z₅* = 5 - 0i, which is 5.

Therefore, the conjugate numbers of 1, 2, 3, 4, and 5 are 1, 2, 3, 4, and 5, respectively.

Remember, the concept of complex conjugates extends to complex numbers with non-zero imaginary parts as well. The process of finding the conjugate remains the same: change the sign of the imaginary part while keeping the real part unchanged.

Feel free to reach out if you have any further questions!