#1. Reduce each of these quantities to a real number 5i (1-2) (2-2) (3-2) (a) 1+2i 3-4i + 2-2 5 i #2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ + 2₂/1² = 2 ( 12₁1 ² + 122 1²). ·/w/=1 and ZW #1. #3. Assuming either 121=1 Prove that =/ Z-W 1-ZW = 1. (b) #4. Show that equation | 2-1-2|=1 Can be written as 121²2 Re Z-2 Imz +1=0. #5. Perform the needed operations. (a) (1+√3i) 10 (b) (-1 + 2)² #6. Find the square roots of (a) 2i; (b) 1-√3 i and express them in rectangular wordinates. #7. Find the four roots of the equation z4+4=0 and use them to factor 24+4 into quadratic factors with real coefficients.
#1. Reduce each of these quantities to a real number 5i (1-2) (2-2) (3-2) (a) 1+2i 3-4i + 2-2 5 i #2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ + 2₂/1² = 2 ( 12₁1 ² + 122 1²). ·/w/=1 and ZW #1. #3. Assuming either 121=1 Prove that =/ Z-W 1-ZW = 1. (b) #4. Show that equation | 2-1-2|=1 Can be written as 121²2 Re Z-2 Imz +1=0. #5. Perform the needed operations. (a) (1+√3i) 10 (b) (-1 + 2)² #6. Find the square roots of (a) 2i; (b) 1-√3 i and express them in rectangular wordinates. #7. Find the four roots of the equation z4+4=0 and use them to factor 24+4 into quadratic factors with real coefficients.
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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please solve number 5
Transcribed Image Text:#. Reduce each of these quantities to a real number
1+2i
si
3-4 i
(1-2) (2-2) (3-2)
(a)
+
2-2
5 i
(b)
#2. If 2₁ and 2₂ are two complex numbers, show that
12₁-221² + 12₁ +2₂1² = 2 ( 121₁1² + 122 1²).
#3. Assuming either /2/=1 or | w/=1 and ZW 1.
Prove that
Z-W
= 1.
1-ZW
#4. Show that equation | 2-1-2|=1 Can be written as
121²2 Re Z-2 Imz +1=0.
#5. Perform the needed operations.
(a) (1+√3i) 10
(b) (-1+i)7
#6. Find the square roots of (a) 2i; (b) 1-√3 i and
express them in rectangular wordinates.
#7. Find the four roots of the equation Z² +4=0 and
use them to factor z4+4 into quadratic factors with
real wefficients.
#8. In each case, sketch the set of points determined by
the given conditiong
(a) /2-1+2/>1
(b) Re(iz) < -1.
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