what is the conjugate of 6-3i
What is the conjugate of 6-3i?
Answer:
- Introduce the Concept: In complex numbers, a conjugate is a value that is derived from a complex number by changing the sign of its imaginary part. Understanding the concept of a conjugate is essential when performing operations with complex numbers, such as addition, subtraction, multiplication, and division.
Step 1: Present the Concept
- A complex number is typically written in the form a + bi, where a is the real part, and bi is the imaginary part.
- The conjugate of a complex number a + bi is written as a - bi. This involves flipping the sign of the imaginary part while keeping the real part unchanged.
Step 2: Apply the Concept to the Given Number
- In this case, the given complex number is 6 - 3i.
- Here, 6 represents the real part, and -3i represents the imaginary part.
- To find the conjugate, invert the sign of the imaginary part, resulting in 6 + 3i.
Step 3: Verify the Solution
- Check your result: The original complex number is 6 - 3i, and its conjugate is correctly calculated as 6 + 3i.
- Since only the sign of the imaginary part changes, the conjugate calculation is validated by observing that the real part remains constant.
Final Answer:
The conjugate of 6 - 3i is 6 + 3i.