et z = 4 + 4√√/3i.. (a) Graph z in the complex plane. Im 8 6 4 2 Im 3.5 3.0 2.5 2.0 1.5 1.0 0.5 2 4 0.5 (b) Write z in polar form. 6 1.0 8 10 12 14 1.5 2.0 Re Re 2.0 Im 1.5 1.0 E 0.5 14 12 10 Im 4 10 15 Re R
et z = 4 + 4√√/3i.. (a) Graph z in the complex plane. Im 8 6 4 2 Im 3.5 3.0 2.5 2.0 1.5 1.0 0.5 2 4 0.5 (b) Write z in polar form. 6 1.0 8 10 12 14 1.5 2.0 Re Re 2.0 Im 1.5 1.0 E 0.5 14 12 10 Im 4 10 15 Re R
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![The image contains a mathematical exercise involving complex numbers, presented in an educational format. Two graphs and a set of questions are included.
**Graphs:**
1. **Graph on the Left:**
- **Axes:** The y-axis is labeled "Im" (Imaginary) and the x-axis is labeled "Re" (Real).
- **Plot:** A single point is plotted at approximately (1, 2) on the graph.
2. **Graph on the Right:**
- **Axes:** The y-axis is labeled "Im" (Imaginary) and the x-axis is labeled "Re" (Real).
- **Plot:** A single point is plotted at approximately (4, 8) on the graph.
**Questions:**
**(b)** Write \( z \) in polar form.
\[ z = \underline{\hspace{3cm}} \]
**(c)** Find the complex number, \( z^9 \). (Enter your answer in \( a + bi \) form.)
\[ z^9 = \underline{\hspace{3cm}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61d8af2b-7fdf-4a8e-a1bf-75f5ea698050%2F3e46e866-a114-4177-83a4-2a30df8d7807%2Fynxn6g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical exercise involving complex numbers, presented in an educational format. Two graphs and a set of questions are included.
**Graphs:**
1. **Graph on the Left:**
- **Axes:** The y-axis is labeled "Im" (Imaginary) and the x-axis is labeled "Re" (Real).
- **Plot:** A single point is plotted at approximately (1, 2) on the graph.
2. **Graph on the Right:**
- **Axes:** The y-axis is labeled "Im" (Imaginary) and the x-axis is labeled "Re" (Real).
- **Plot:** A single point is plotted at approximately (4, 8) on the graph.
**Questions:**
**(b)** Write \( z \) in polar form.
\[ z = \underline{\hspace{3cm}} \]
**(c)** Find the complex number, \( z^9 \). (Enter your answer in \( a + bi \) form.)
\[ z^9 = \underline{\hspace{3cm}} \]
![**Complex Number Representation**
Let \( z = 4 + 4 \sqrt{3}i \).
**(a) Graph \( z \) in the complex plane.**
The following diagrams represent the point \( z \) in different scales of the complex plane.
1. **Top Left Graph:**
- The horizontal axis (Re) is labeled from 0 to 14 in increments of 2.
- The vertical axis (Im) is labeled from 0 to 8 in increments of 2.
- The point is located at approximately (4, 6.93) on the graph.
2. **Top Right Graph:**
- The horizontal axis (Re) spans from 0 to 15 in increments of 5.
- The vertical axis (Im) spans from 0 to 2 in increments of 0.5.
- The point appears around (4, 1.73) on this graph.
3. **Bottom Graph:**
- The horizontal axis (Re) ranges from 0 to 2 in increments of 0.5.
- The vertical axis (Im) ranges from 0 to 3.5 in increments of 0.5.
- The point is at approximately (1, 2) on this graph.
**(b) Write \( z \) in polar form.**
[Box provided for polar form entry]
These representations illustrate how the same complex number appears at different scales on the complex plane, allowing for analysis in both rectangular and polar forms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61d8af2b-7fdf-4a8e-a1bf-75f5ea698050%2F3e46e866-a114-4177-83a4-2a30df8d7807%2F7ia5njy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Complex Number Representation**
Let \( z = 4 + 4 \sqrt{3}i \).
**(a) Graph \( z \) in the complex plane.**
The following diagrams represent the point \( z \) in different scales of the complex plane.
1. **Top Left Graph:**
- The horizontal axis (Re) is labeled from 0 to 14 in increments of 2.
- The vertical axis (Im) is labeled from 0 to 8 in increments of 2.
- The point is located at approximately (4, 6.93) on the graph.
2. **Top Right Graph:**
- The horizontal axis (Re) spans from 0 to 15 in increments of 5.
- The vertical axis (Im) spans from 0 to 2 in increments of 0.5.
- The point appears around (4, 1.73) on this graph.
3. **Bottom Graph:**
- The horizontal axis (Re) ranges from 0 to 2 in increments of 0.5.
- The vertical axis (Im) ranges from 0 to 3.5 in increments of 0.5.
- The point is at approximately (1, 2) on this graph.
**(b) Write \( z \) in polar form.**
[Box provided for polar form entry]
These representations illustrate how the same complex number appears at different scales on the complex plane, allowing for analysis in both rectangular and polar forms.
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