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We have two arbitrary complex numbers, a and b. The real and imaginary part of complex number a are denoted as ar and ai. The real and imaginary part of complex number b are denoted as brand b₁. The amplitude and phase of these two complex numbers are a❘ and ea, |b| and b, respectively. In other words, a = a + ja₁ = |a|≤0a, b = br + jb¡ = |b|≤0₁. (a) If ab*, then we must have |a| = |b|. (Q16) (b) If a = b*, then we must have a = 0. (Q17) (c) If a 1/b, then we must have |a| = 1/|b|. (Q18) (d) If a 1/b*, then we must have a = 0 b. (Q19) = Problem 2 (3 pts each). The following statements may or may not be always correct. If they are always correct, prove them using methods you learned in class. If not, find at least one counter- example.

We have two arbitrary complex numbers, a and b. The real and imaginary part of complex number a are denoted as ar and ai. The real and imaginary part of complex number b are denoted as brand b₁. The amplitude and phase of these two complex numbers are a❘ and ea, |b| and b, respectively. In other words, a = a + ja₁ = |a|≤0a, b = br + jb¡ = |b|≤0₁. (a) If ab*, then we must have |a| = |b|. (Q16) (b) If a = b*, then we must have a = 0. (Q17) (c) If a 1/b, then we must have |a| = 1/|b|. (Q18) (d) If a 1/b*, then we must have a = 0 b. (Q19) = Problem 2 (3 pts each). The following statements may or may not be always correct. If they are always correct, prove them using methods you learned in class. If not, find at least one counter- example.

Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
10th Edition
ISBN:9781337399128
Author:Russell E. Smith
Publisher:Russell E. Smith
Chapter17: Commercial And Industrial Air-conditioning Control Systems
Section: Chapter Questions
Problem 22RQ
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We have two arbitrary complex numbers, a and b. The real and imaginary part of complex number a are denoted as ar and ai. The real and imaginary part of complex number b are denoted as brand b₁. The amplitude and phase of these two complex numbers are a❘ and ea, |b| and b, respectively. In other words, a = a + ja₁ = |a|≤0a, b = br + jb¡ = |b|≤0₁. (a) If ab*, then we must have |a| = |b|. (Q16) (b) If a = b*, then we must have a = 0. (Q17) (c) If a 1/b, then we must have |a| = 1/|b|. (Q18) (d) If a 1/b*, then we must have a = 0 b. (Q19) =
Transcribed Image Text:We have two arbitrary complex numbers, a and b. The real and imaginary part of complex number a are denoted as ar and ai. The real and imaginary part of complex number b are denoted as brand b₁. The amplitude and phase of these two complex numbers are a❘ and ea, |b| and b, respectively. In other words, a = a + ja₁ = |a|≤0a, b = br + jb¡ = |b|≤0₁. (a) If ab*, then we must have |a| = |b|. (Q16) (b) If a = b*, then we must have a = 0. (Q17) (c) If a 1/b, then we must have |a| = 1/|b|. (Q18) (d) If a 1/b*, then we must have a = 0 b. (Q19) =
Problem 2 (3 pts each). The following statements may or may not be always correct. If they are always correct, prove them using methods you learned in class. If not, find at least one counter- example.
Transcribed Image Text:Problem 2 (3 pts each). The following statements may or may not be always correct. If they are always correct, prove them using methods you learned in class. If not, find at least one counter- example.
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