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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: Are the absolute values of a complex number and its conjugate always equal?
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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.


Which arithmetic operation requires the use of the complex conjugate?

It can be used as a convenient shortcut to calculate the absolute value of the square of a complex number. Just multiply the number by its complex conjugate.I believe it has other uses as well.


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

Related questions

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 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.


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 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.


What is the complex conjugate complex number-8-6i?

-6i-8


Does every real number equal its complex conjugate?

Yes they do, complex conjugate only flips the sign of the imaginary part.


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 a real number?

Since the imaginary portion of a real number is zero, the complex conjugate of a real number is the same number.


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.


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)

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