666 Worked-Out Solutions to Exercises: Chapters 21 to 29
(b) To find the difference (4 +j5)− (3 −j8), we multiply the second complex number
through by −1, and then add the real parts and the imaginary parts separately, getting(4+j5)− (3 −j8)= (4 +j5)+ [−1(3−j8)]
= (4 +j5)+ (− 3 +j8)
= (4 − 3) +j(5+ 8)
= 1 +j 13(c) To find the product (4 +j5)(3−j8), we use the product of sums rule. This gives us(4+j5)(3−j8)= 4 × 3 + 4 × (−j8)+j 5 × 3 +j 5 × (−j8)
= 12 + (−j32)+j 15 +j×j× (−40)
= 12 + (−j17)+ (−1)× (−40)
= (12 + 40) + (−j17)
= 52 −j 17(d) To find the quotient (4 +j5) / (3 −j8), we use the quotient formula from the text.
If a,b,c, and d are real numbers, and as long as c and d aren’t both equal to 0, then(a+jb) / (c+jd)
= (ac+bd) / (c^2 +d^2 )+j(bc−ad) / (c^2 +d^2 )Table C-1. Solution to Prob. 5 in Chap. 21.
Expression Value
↑ ↑
j^8 1
j^7 −j
j^6 − 1
j^5 j
j^4 1
j^3 −j
j^2 − 1
j^1 j
j^0 1
j−^1 −j
j−^2 − 1
j−^3 j
j−^4 1
j−^5 −j
j−^6 − 1
j−^7 j
j−^8 1
↓ ↓