Podcast
Questions and Answers
What is the result of the operation $2K - 5V$ in the form of $a + bi$?
What is the result of the operation $2K - 5V$ in the form of $a + bi$?
- $18 - 39i$
- $-10 + 8i$
- $-10i + 8$ (correct)
- $-15 - 30i$
What is the product of a complex number $V$ and its complex conjugate?
What is the product of a complex number $V$ and its complex conjugate?
- 36
- 9
- 18
- 45 (correct)
Which of the following represents $V/K$ in simplified form?
Which of the following represents $V/K$ in simplified form?
- $ rac{18 - 39i}{41}$ (correct)
- $ rac{-3 - 6i}{4 + 5i}$
- $ rac{-3 + 6i}{4 - 5i}$
- $ rac{-12 - 15i}{41}$
Which statement correctly shows that $-10 - 2i$ is a zero of the function $g(x) = x^2 + 20x + 104$?
Which statement correctly shows that $-10 - 2i$ is a zero of the function $g(x) = x^2 + 20x + 104$?
What is the standard form of the quadratic function $H(x)$ given that $V$ is a zero?
What is the standard form of the quadratic function $H(x)$ given that $V$ is a zero?
What is the difference quotient for the function $g(x) = -3x^2 + 8x - 7$?
What is the difference quotient for the function $g(x) = -3x^2 + 8x - 7$?
Which of the following transformations confirms that $m(x) = 2(- (x/3)^2) - 7$ is neither even nor odd?
Which of the following transformations confirms that $m(x) = 2(- (x/3)^2) - 7$ is neither even nor odd?
What are the x-intercepts of the 6th degree polynomial function $P(x)$ with real number coefficients having zeros $5$, $7i$, $-11$, and $6i + 9$?
What are the x-intercepts of the 6th degree polynomial function $P(x)$ with real number coefficients having zeros $5$, $7i$, $-11$, and $6i + 9$?
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Study Notes
Complex Number Operations
- Multiplying complex numbers involves using the distributive property, foil, and simplifying terms.
- Adding and Subtracting complex numbers involves combining real and imaginary components.
- Dividing complex numbers involves multiplying the numerator and denominator by the complex conjugate of the denominator to eliminate the imaginary component in the denominator.
Complex Number Properties
- The product of a complex number and its conjugate is a real number.
- The square root of -1 is represented by the imaginary unit 'i'.
- The conjugate of a complex number is obtained by changing the sign of its imaginary component.
Quadratic Functions
- A quadratic function can be written in standard form.
- Given a zero of a quadratic function, the corresponding factor can be obtained using the complex conjugate property.
- A quadratic function can be determined using a point and one of its zeros.
Finding Zeros of a Function
- Substituting a value into a function to check if it produces a zero can confirm it's a zero.
- Factoring a quadratic function can reveal its zeros.
- Quadratic formula can be used to find the zeros of a quadratic function.
Function Transformations
- A parent function m(x) can be transformed by applying operations.
- To determine if a function is even or odd, evaluate f(-x) and compare with f(x) for all values of x.
- If f(-x) = f(x), the function is even. If f(-x) = -f(x), the function is odd.
Simplifying Expressions
- Simplify radical expressions involving complex numbers by factoring out 'i' and using the property √-1 = i.
Difference Quotient
- The difference quotient of a function g(x) is the expression [g(x+h) - g(x)]/h.
- It represents the average rate of change of the function over an interval of length h.
Polynomial Functions
- A polynomial function of degree n has n zeros, counting multiplicity.
- If a polynomial function has real number coefficients, its complex zeros must appear in conjugate pairs.
- The number of x-intercepts a polynomial function has is equal to the number of real zeros.
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