Match each description when z = 9 + 3i. 1. Real part of z 2. Imaginary part of z 3. Complex conjugate of z 4. 3i - z 5. z - 9 6.
1 answer:
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Answer:
Domain: All Real Numbers
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule:
Derivative:
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = ln(2x² + 1)
<u>Step 2: Differentiate</u>
- Derivative ln(u) [Chain Rule/Basic Power]:
- Simplify:
- Multiply:
<u>Step 3: Domain</u>
We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.
Therefore, our domain would be all real numbers.
We can also graph the differential function to analyze the domain.
Answers:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
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Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as
Applying this rule to the three given points will mean....
- Point A = (-2, 3) becomes A ' = (-2, -3)
- Point B = (0, 3) becomes B ' = (0, -3)
- Point C = (-1, -1) becomes C ' = (-1, 1)
The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
