Further Maths - Conjugates
Conjugates
A pair of complex numbers with a different sign but otherwise the same values are called conjugates:
\[3 + 4i 3 - 4i\]What are complex conjugates?
A pair of complex numbers with real and imaginary parts equal in magnitude but opposite in sign:
- $a+bi$ and $a-bi$
What is a pair of complex numbers $a+bi$ and $a-bi$ called?
A complex conjugate.
What is the result of multipling complex conjugates?
You get a real number.
What other topic links to multiplying complex conjugates?
The difference of two squares.
What is the result of adding complex conjugates?
- You get a real number.
- $(a+bi)+(a-bi) = 2a$
What is the result of subtracting complex conjugates?
- You get an imaginary number.
- $(a+bi)-(a-bi) = 2bi$
How can you divide complex numbers?
- Using complex conjugation to convert the denominator to a real number
- Multiply the top and bottom by the complex conjugate of the denominator