0
Oh, isn't that just a happy little question? The complex conjugate of a real number like 8 is just 8 itself because there is no imaginary part to change. Just like how every tree needs its roots, every real number needs its complex conjugate to stay balanced and harmonious. Just remember, there are no mistakes, only happy little accidents in math!
Still curious? Ask our experts.
Chat with our AI personalities
Judy
Professor
Ezra
Add your answer:
Earn +20 pts
What is the complex conjugate of 8 plus 8i?
8 - 8i
What is conjugate function?
If you have a complex function in the form "a+ib", the (complex) conjugate is "a-ib". "Conjugate" is usually a function that the original function must be multiplied by to achieve a real number.
What is the meaning of Complex conjugate reflection?
For a complex number (a + bi), its conjugate is (a - bi). If the number is graphically plotted on the Complex Plane as [a,b], where the Real number is the horizontal component and Imaginary is vertical component, the Complex Conjugate is the point which is reflected across the real (horizontal) axis.
Is the sum of two conjugate complex number a real number?
Not necessarily. It can be wholly imaginary.For example, 1 + i actually has two complex conjugates. Most schools will teach you that the complex conjugate is 1 - i. However, -1 + i is also a conjugate for 1 + i. (Their product is -1 times the product of the "normal" conjugate pair).The sum of 1 + i and -1 + i = 2i
What is the usefulness of the conjugate and its effect on other complex numbers?
The conjugate of a complex number is the same number (but the imaginary part has opposite sign). e.g.: A=[5i - 2] --> A*=[-5i - 2] Graphically, as you change the sign, you also change the direction of that vector. The conjugate it's used to solve operations with complex numbers. When a complex number is multiplied by its conjugate, the product is a real number. e.g.: 5/(2-i) --> then you multiply and divide by the complex conjugate (2+i) and get the following: 5(2+i)/(2-i)(2+i)=(10+5i)/5=2+i
