What transformations change the graph F(x) to the graph g(x)

Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"

Flura [38]

1. 12(x − 4)
2. x5
3. The quotient of some number and ten
4. b − 8
5. The quotient of four times some number and six
6. 3x + 7

1. x and -4 are multiplied by 12
2 raided to this 5th power is an exponent
3 quotient means division
4 less than means subtraction
5 division means quotient, list numerator first then the denominator
6 product of is multiplication and more is an addition.

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3 years ago

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Explain and demonstrate the multiplication of complex conjugates using 2+3i and its complex conjugate. Be sure to discuss all st

krok68 [10]

The product of a complex number and its conjugate is (a + i b) · (a - i b), where a and b are real numbers, and the result for the complex number 2 + i 3 is 13.

<h3>What is the multiplication of a complex number and its conjugate</h3>

Let be a complex number a + i b, whose conjugate is a - i b. Where a and b are real numbers. The product of these two numbers is:

(a + i b) · (a - i b)

Then, we proceed to obtain the result by some algebraic handling:

a · (a + i b) + (- i b) · (a + i b)

a² + i a · b - i a · b - i² b²

a² - i² b²

a² + b²

If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:

$z\cdot \bar z = 2^{2} + 3^{2}$