1. Prove that the set of complex numbers, together with complex number addition and multiplication is a field. 2. Evaluate a) i2021 b) i1.000,000 3. Write the following in the form a + ib. a) 2+3i – 4i3 + 51® b) 4-+ 5? - c) (2 – 5i) ) 213 3-S d) 5-313+i 4. Find: a) Re[) b) Im n-D(1-j?)(1-i³)] c) If z = x + iy, find Re[(1 + i)z] d) If z = x + iy, find Im(z² + z?) 5. Find z in the given equations. 2-i a) z+ 22z = 1+31 iz, - izz = 2+ 10i b) {-z, + (1 – i)z2 = 3 – 5i 6. Prove that c z,Zz + Z,Zz = 2Re(z,Z2).
1. Prove that the set of complex numbers, together with complex number addition and multiplication is a field. 2. Evaluate a) i2021 b) i1.000,000 3. Write the following in the form a + ib. a) 2+3i – 4i3 + 51® b) 4-+ 5? - c) (2 – 5i) ) 213 3-S d) 5-313+i 4. Find: a) Re[) b) Im n-D(1-j?)(1-i³)] c) If z = x + iy, find Re[(1 + i)z] d) If z = x + iy, find Im(z² + z?) 5. Find z in the given equations. 2-i a) z+ 22z = 1+31 iz, - izz = 2+ 10i b) {-z, + (1 – i)z2 = 3 – 5i 6. Prove that c z,Zz + Z,Zz = 2Re(z,Z2).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![14:20 A d
ll ll
Problem Set 1.pdf
Republic of the Philippines
PANGASINAN STATE UNIVERSITY
Urdaneta City Campus
COMPLEX ANALYSIS
PROBLEM SET 1
1. Prove that the set of complex numbers, together with complex number addition and multiplication
is a field.
2. Evaluate
a) į2021
b) i1.000,000
3. Write the following in the form a + ib.
a) 2+3i – 413 + 5i8
b) 4 -+ 513 –
c) (2 – 5i) )
3-51
d)
5-31+i
4. Find:
a) Re )
b) Im-a-pa-)
c) If z = x + iy, find Re[(1 + i)z]
d) If z = x + iy, find Im(2? +z2)
5. Find z in the given equations.
a) z+ 22z =
1+31
izz - izz = 2 + 10i
l-z1 + (1 – i)z2 = 3 – 5i
6. Prove that c z,zz + Z,Zz = 2Re(z,Z2).
b)
1 of 1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F558d51dc-ee2c-4f9a-b387-4ae74b531fd2%2F0b08ee4f-d637-4183-9217-ea3b0290e3f2%2Fb2090hc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:14:20 A d
ll ll
Problem Set 1.pdf
Republic of the Philippines
PANGASINAN STATE UNIVERSITY
Urdaneta City Campus
COMPLEX ANALYSIS
PROBLEM SET 1
1. Prove that the set of complex numbers, together with complex number addition and multiplication
is a field.
2. Evaluate
a) į2021
b) i1.000,000
3. Write the following in the form a + ib.
a) 2+3i – 413 + 5i8
b) 4 -+ 513 –
c) (2 – 5i) )
3-51
d)
5-31+i
4. Find:
a) Re )
b) Im-a-pa-)
c) If z = x + iy, find Re[(1 + i)z]
d) If z = x + iy, find Im(2? +z2)
5. Find z in the given equations.
a) z+ 22z =
1+31
izz - izz = 2 + 10i
l-z1 + (1 – i)z2 = 3 – 5i
6. Prove that c z,zz + Z,Zz = 2Re(z,Z2).
b)
1 of 1
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