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Yes. This is easy to prove; in the following, I'll use "^" for powers. Let the complex number be (a + bi), then its conjugate, by definition, is (a - bi). Multiplying them, you get a^2 + abi - abi + bi^2 = a^2 + bi^2 = a^2 - b^2 (since i^2 = -1).Update: One interesting, and quite useful, property is that the product of the complex number and its conjugate is equal to the square of the absolute value of the complex number.
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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
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
Conjugate and a complex number equal?
The conjugate will have equal magnitude. The angle from the real axis will be the same angle measure (but opposite direction).
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 a complex number and its conjugate a real or imaginary number?
Their sum is real.
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 graphical relationship between a conjugate number and a complex number?
Graphically, the conjugate of a complex number is its reflection on the real axis.
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.
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
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 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.
Conjugate and a complex number equal?
The conjugate will have equal magnitude. The angle from the real axis will be the same angle measure (but opposite direction).
Graphs of a complex number and its conjugate?
The graph of a complex number and its conjugate in the complex plane are reflections of each other across the real axis. If a complex number is represented as z = a + bi, its conjugate z* is a - bi. This symmetry across the real axis is a property of the complex conjugate relationship.
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 a complex number and its conjugate a real or imaginary number?
Their sum is real.
What effect does a congugate have on other complex numbers?
A number multiplied by its complex conjugate will result in a real number. Also, adding a number to its conjugate will result in a real number. But typically the multiplication is what is used.
