The conjugate of a complex number is found by changing the sign of its imaginary part. For the complex number 7 + 2i, the conjugate is calculated as follows:
- Identify the real part: 7
- Identify the imaginary part: 2i
To find the conjugate, simply change the sign of the imaginary part:
| Complex Number | Conjugate |
|---|---|
| 7 + 2i | 7 – 2i |
Thus, the conjugate of 7 + 2i is 7 – 2i.
Understanding the conjugate is essential because it is used in various mathematical operations, such as rationalizing the denominator in fractions or simplifying complex expressions. The conjugate maintains the same real part while reflecting the imaginary part across the real axis, making it a fundamental concept in complex number theory.