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Is the product of two conjugate complex number always a real number?
Wiki User
∙ 12y ago
Yes. This can be verified by using a "generic" complex number, and multiplying it by its conjugate:
(a + bi)(a - bi) = a2 -abi + abi + b2i2 = a2 - b2
Alternative proof:
I'm going to use the * notation for complex conjugate. Any complex number w is real if and only if w=w*. Let z be a complex number. Let w = zz*. We want to prove that w*=w. This is what we get:
w* = (zz*)*
= z*z** (for any u and v, (uv)* = u* v*)
= z*z
= w
Wiki User
∙ 12y ago
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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)
What is self conjugate of complex number?
Aamir jamal; All real numbers are complex numbers with 0 as its imaginary part.A real number is self-conjugate. e.g;a+0i self conjugate =a-0i i=iota
What is the conjugate of the complex number 7-4i?
To get the conjugate simply reverse the sign of the complex part. Thus conj of 7-4i is 7+4i
What is the conjugate of 100?
"Conjugate" usually means that in one of two parts, the sign is changed - as in a complex conjugate. If the second part is missing, the conjugate is the same as the original number - in this case, 100.
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 product of the complex number a plus bi and its conjugate?
The product is a^2 + b^2.
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
Are the absolute values of a complex number and its conjugate always equal?
yes
How do conjugate arrive at complex number?
Complex numbers form: a + bi where a and b are real numbers. The conjugate of a + bi is a - bi If you multiply a complex number by its conjugate, the product will be a real number, such as (a + bi)(a - bi) = a2 - (bi)2 = a2 - b2i2 = a2 - b2(-1) = a2 + b2
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.
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
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.
How a real number is itself conjugate?
Assuming that the question is in the context of complex number, the product of any real number with itself (its square) is a real number.
How a real number is self conjugate?
Assuming that the question is in the context of complex number, the product of any real number with itself (its square) is 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.
