Problem 1. 1.1. Find a, b, r, ER satisfying the following two identities, where r> 0 and θεσ—π,π]: 3-5i 4 + 3i 2) i) 22 (1 + i)(√3+i)=re", 2√2 where we recall that e is the complex number cos 0 + i sin 0. = a + bi
Problem 1. 1.1. Find a, b, r, ER satisfying the following two identities, where r> 0 and θεσ—π,π]: 3-5i 4 + 3i 2) i) 22 (1 + i)(√3+i)=re", 2√2 where we recall that e is the complex number cos 0 + i sin 0. = a + bi
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 46E
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![Problem 1.
1.1. Find a, b, r, ER satisfying the following two identities, where r > 0 and
0 € (-π, π]:
z)
3-5i
4 + 3i
= a + bi
ii) 22(1 + i)(√3+i)= reo,
2√2
where we recall that ei is the complex number cos 0 + i sin 0.
1.2. Show that, for any z, w E C, we have zw=zw. Use this identity to conclude
that |zw|=|z||w|.
1.3. Find 5 distinct complex numbers z EC satisfying 2 = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0a3c19f-0ecb-43ef-8f62-48070c8bcd56%2F62a32343-04a2-41a7-8cae-7dc1ec2b22f6%2Ficoguj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1.
1.1. Find a, b, r, ER satisfying the following two identities, where r > 0 and
0 € (-π, π]:
z)
3-5i
4 + 3i
= a + bi
ii) 22(1 + i)(√3+i)= reo,
2√2
where we recall that ei is the complex number cos 0 + i sin 0.
1.2. Show that, for any z, w E C, we have zw=zw. Use this identity to conclude
that |zw|=|z||w|.
1.3. Find 5 distinct complex numbers z EC satisfying 2 = 1.
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