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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 else can I help you with?
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 2 numbers multiply to make 249 and add to 7?
The complex conjugate pair3.5 - 15.387iand3.5 + 15.387iwhere i is the imaginary square root of -1.
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 conjugate of 11 plus 5i?
To find the complex conjugate change the sign of the imaginary part: For 11 + 5i the complex conjugate is 11 - 5i.
How do you simplify a complex fraction?
You multiply the numerator and the denominator of the complex fraction by the complex conjugate of the denominator.The complex conjugate of a + bi is a - bi.
How do you simplify complexed fractions?
You multiply the numerator and the denominator of the complex fraction by the complex conjugate of the denominator.The complex conjugate of a + bi is a - bi.
When dividing complex numbers the first step is to multiply top and bottom by the conjugate of the denominator?
complex
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 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
Complex conjugate of 5i-4?
To get the complex conjugate, change the sign in front of the imaginary part. Thus, the complex conjugate of -4 + 5i is -4 - 5i.
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
What is the complex conjugate of 2-3i?
The complex conjugate of 2-3i is 2+3i.
What is the complex conjugate 3i plus 4?
The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. For the complex number ( 3i + 4 ), which can be expressed as ( 4 + 3i ), the complex conjugate is ( 4 - 3i ).
What can you add to get 7 but multiply to get 120?
127
What can you add to get 19 and multiply to get 216?
235
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.
