This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back POPOOLA — missed you this week. To show the value of the given expression, we will simplify it step-by-step. The expression is: 25 ( (1+j3)/(3+j4) - (2-j5)/(j) ) Step 1: Simplify the first fraction (1+j3)/(3+j4). To simplify a complex fraction, multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 3+j4 is 3-j4. (1+j3)/(3+j4) = (1+j3)/(3+j4) × (3-j4)/(3-j4) Multiply the numerators: (1+j3)(3-j4) = 1(3) + 1(-j4) + j3(3) + j3(-j4) = 3 - j4 + j9 - j^212 Since j^2 = -1: = 3 + j5 - (-1)12 = 3 + j5 + 12 = 15 + j5 Multiply the denominators: (3+j4)(3-j4) = 3^2 - (j4)^2 = 9 - j^216 = 9 - (-1)16 = 9 + 16 = 25 So, the first fraction simplifies to: (15+j5)/(25) = (15)/(25) + (j5)/(25) = (3)/(5) + j(1)/(5) Step 2: Simplify the second fraction (2-j5)/(j). To simplify this fraction, multiply the numerator and denominator by -j. (2-j5)/(j) = (2-j5)/(j) × (-j)/(-j) Multiply the numerators: (2-j5)(-j) = -j2 + j^25 Since j^2 = -1: = -j2 + (-1)5 = -5 - j2 Multiply the denominators: j(-j) = -j^2 = -(-1) = 1 So, the second fraction simplifies to: (-5-j2)/(1) = -5 - j2 Step 3: Subtract the second simplified fraction from the first. ( (3)/(5) + j(1)/(5) ) - (-5 - j2) = (3)/(5) + j(1)/(5) + 5 + j2 Combine the real parts: (3)/(5) + 5 = (3)/(5) + (25)/(5) = (28)/(5) Combine the imaginary parts: j(1)/(5) + j2 = j(1)/(5) + j(10)/(5) = j(11)/(5) So, the expression inside the parenthesis is: (28)/(5) + j(11)/(5) Step 4: Multiply the result by 25. 25 ( (28)/(5) + j(11)/(5) ) = 25 × (28)/(5) + 25 × j(11)/(5) = 5 × 28 + 5 × j11 = 140 + j55 The simplified expression is: 140 + j55 Drop the next question.