What is the conjugate of 6-3i

General
1

what is the conjugate of 6-3i

2

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.