To describe the transformation applied to point z to obtain point w in the complex plane for the given operation.
2 Units to the right and down 3 units
Given:
The given operation is w = z + ( 2 − 3 i )
Calculation:
The transformation w = z + ( 2 − 3 i ) translate 2 units to the right and down 3 units because it adds 2 the x component and − 3 to the y component.
To describe the transformation applied to point z to obtain point w in the complex plane for the given operation.
90 ∘ Counter clockwise.
Given:
The given operation is w = i ⋅ z
Calculation:
The transformation w = i ⋅ z rotates z , 90 ∘ counter clockwise.
To describe the transformation applied to point z to obtain point w in the complex plane for the given operation.
Dilation by a factor of 3 .
Given:
The given operation is w = 3 z
Calculation:
The transformation w = 3 z dilates z by a factor of 3 .
To describe the transformation applied to point z to obtain point w in the complex plane for the given operation.
Reflection of z about the real axis.
Given:
The given operation- w is the conjugate of z
Calculation:
Reflect z about the real axis because change the y component to − y .
To describe the transformation applied to point
Given:
The given operation is
Calculation:
The transformation
To describe the transformation applied to point
Given:
The given operation is
Calculation:
The transformation
To describe the transformation applied to point
Dilation by a factor of
Given:
The given operation is
Calculation:
The transformation
To describe the transformation applied to point
Reflection of
Given:
The given operation-
Calculation:
Reflect
To find the rectangular form of these vectors.
Answer to Problem 44E
Explanation of Solution
Given:
The given operation is
Calculation:
The transformation
To describe the transformation applied to point
Answer to Problem 44E
Explanation of Solution
Given:
The given operation is
Calculation:
The transformation
To describe the transformation applied to point
Answer to Problem 44E
Explanation of Solution
Given:
The given operation is
Calculation:
The transformation
To describe the transformation applied to point
Answer to Problem 44E
Dilation by a factor of
Explanation of Solution
Given:
The given operation is
Calculation:
The transformation
To describe the transformation applied to point
Answer to Problem 44E
Reflection of
Explanation of Solution
Given:
The given operation-
Calculation:
Reflect
To add the two
Answer to Problem 44E
Explanation of Solution
Given:
The phasors for these two expressions are written as
Calculation:
Adding the two vectors as follows-
To write the sum of two vectors in phasor notation.
Answer to Problem 44E
Explanation of Solution
Given:
The phasors for these two expressions are written as
Calculation:
It is given that
Now it can be concluded that-
Therefore the phasor notation is
To write the sinusoidal expression corresponding to the phasor in part c.
Answer to Problem 44E
Explanation of Solution
Given:
The phasors for these two expressions are written as
Calculation:
The sinusoidal expression corresponding to that phasor in part c is-
Chapter 9 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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