0
Are the absolute values of a complex number and its conjugate always equal?
Wiki User
∙ 14y ago
yes
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
If a and b are any real numbers what is the conjugate of a plus b?
The concept of conjugate is usually used in complex numbers. If your complex number is a + bi, then its conjugate is a - bi.
What is the absolute value of a complex number?
The absolute value of a complex number a+bi is the square root of (a2+b2). For example, the absolute value of 4+9i is the square root of (42 + 92) which is the square root of 97 which is about 9.8489 (The absolute value of a complex number is not complex.)
Why do you multiply by the complex conjugate?
Whenever a complex number (a + bi) is multiplied by it's conjugate (a - bi), the result is a real number: (a + bi)* (a - bi) = a2 - abi + abi - (bi)2 = a2 - b2i2 = a2 - b2(-1) = a2 + b2 This is useful when dividing complex numbers, because the numerator and denominator can both be multiplied by the denominator's conjugate, to give an equivalent fraction with a real-number denominator.
What is -4-3i divided by 4 plus i?
To divide by a complex number, write it as a fraction and then multiply the numerator and denominator by the complex conjugate of the denominator - this is formed by changing the sign of the imaginary bit of the number; when a complex number (a + bi) is multiplied by its complex conjugate the result is the real number a² + b² which can be divided into the complex number of the numerator: (-4 - 3i) ÷ (4 + i) = (-4 - 3i)/(4 + i) = ( (-4 - 3i)×(4 - i) ) / ( (4 + i)×(4 - i) ) = (-16 + 4i - 12i + 3i²) / (4² + 1²) = (-16 - 8i - 3) / (16 + 1) = (-19 - 8i)/17
How do you rationalise the denominator?
It depends on what the denominator was to start with: a surd or irrational or a complex number. You need to find the conjugate and multiply the numerator by this conjugate as well as the denominator by the conjugate. Since multiplication is by [conjugate over conjugate], which equals 1, the value is not affected. If a and b are rational numbers, then conjugate of sqrt(b) = sqrt(b) conjugate of a + sqrt(b) = a - sqrt(b), and conjugate of a + ib = a - ib where i is the imaginary square root of -1.
What is the graphical relationship between a conjugate number and a complex number?
Graphically, the conjugate of a complex number is its reflection on the real axis.
Which operation involves complex numbers requires the use of a conjugate to be carried out?
One operation that is used a lot in quantum mechanics is taking the absolute value of the square of a complex number. This is equivalent to multiplying the complex number by its complex conjugate - and doing this is simpler in practice.
What is the relationship between a complex number and its conjugate?
When a complex number is multiplied by its conjugate, the product is a real number and the imaginary number disappears.
What is the complex conjugate of the following complex number 7 plus 5i?
The conjugate is 7-5i
What is complex conjugate for the number 9-5i?
The conjugate is 7 - 3i is 7 + 3i.
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.
If a and b are any real numbers what is the conjugate of a plus b?
The concept of conjugate is usually used in complex numbers. If your complex number is a + bi, then its conjugate is a - bi.
Does every real number equal its complex conjugate?
Yes they do, complex conjugate only flips the sign of the imaginary part.
What is the complex conjugate complex number-8-6i?
-6i-8
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 conjugate of a real number?
Since the imaginary portion of a real number is zero, the complex conjugate of a real number is the same number.
Is the difference of a complex number and it's conjugate an imaginary number?
Yes. By definition, the complex conjugate of a+bi is a-bi and a+bi - (a - bi)= 2bi which is imaginary (or 0)
