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#2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ +221² = 2 ( 1211² + 122 1²).

#2. If 2₁ and 2₂ are two complex numbers, show that 12₁-221² + 12₁ +221² = 2 ( 1211² + 122 1²).

Advanced Engineering Mathematics
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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#. 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.
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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