Final answer:
The Complex Conjugate Theorem states that the conjugate of a complex number can be obtained by changing the sign of its imaginary part. It is important in algebra, analysis, and complex analysis and is used to simplify expressions and perform operations with complex numbers.
Step-by-step explanation:
The Complex Conjugate Theorem is a mathematical concept in complex numbers. It states that for any complex number, its conjugate can be obtained by changing the sign of its imaginary part. This means that if a complex number is of the form a + bi, its conjugate will be a - bi. For example, the conjugate of 3 + 4i is 3 - 4i.
The Complex Conjugate Theorem is important in many areas of mathematics, particularly in algebra, analysis, and complex analysis. It is often used to simplify expressions involving complex numbers, to solve equations, and to perform operations like addition, subtraction, multiplication, and division of complex numbers.
To find the conjugate of a complex number, you simply change the sign of its imaginary part. For example, to find the conjugate of 2 + 5i, you change the sign of 5i to get 2 - 5i.