4. Verify that √2 |z| ≥ |Rez| + |Im zl. Suggestion: Reduce this inequality to (x] - [y])² ≥ 0. 5. In each case, sketch the set of points determined by the given condition: (a) |z − 1 + i] = 1; (b) |z+i| ≤ 3; (c) |z- 4i| ≥ 4.
4. Verify that √2 |z| ≥ |Rez| + |Im zl. Suggestion: Reduce this inequality to (x] - [y])² ≥ 0. 5. In each case, sketch the set of points determined by the given condition: (a) |z − 1 + i] = 1; (b) |z+i| ≤ 3; (c) |z- 4i| ≥ 4.
Chapter3: Functions
Section3.6: Absolute Value Functions
Problem 7SE: Describe the situation in which the distance that point x is from 10 is at least 15 units, Express...
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![4. Verify that √2 |z| ≥ |Rez| + |Im z].
Suggestion: Reduce this inequality to ([x] - [y])² ≥ 0.
5. In each case, sketch the set of points determined by the given condition:
(a) |z −1+ i] = 1;
(b) |z+i| ≤ 3;
(c) |z − 4i| ≥ 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fead15ed3-ba6a-41c2-9d2a-a187cc2ccb25%2F04764875-80d6-4bd8-9d57-1b6379c75b16%2Fr67nkb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Verify that √2 |z| ≥ |Rez| + |Im z].
Suggestion: Reduce this inequality to ([x] - [y])² ≥ 0.
5. In each case, sketch the set of points determined by the given condition:
(a) |z −1+ i] = 1;
(b) |z+i| ≤ 3;
(c) |z − 4i| ≥ 4.
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