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
Assuming j represents the imaginary unit, where j^2 = -1. a) Evaluate j^8 Step 1: Rewrite j^8 using j^2. j^8 = (j^2)^4 Step 2: Substitute j^2 = -1. (j^2)^4 = (-1)^4 Step 3: Calculate the power. (-1)^4 = 1 The value of j^8 is 1. b) Evaluate -(1)/(j^7) Step 1: Simplify the denominator j^7. j^7 = j^4 · j^3 = (j^2)^2 · j^2 · j = (1) · (-1) · j = -j Alternatively, j^7 = j^4 · j^3 = 1 · j^3 = j^3 = j^2 · j = -1 · j = -j. Step 2: Substitute the simplified denominator into the expression. -(1)/(j^7) = -(1)/(-j) = (1)/(j) Step 3: Rationalize the denominator by multiplying the numerator and denominator by j. (1)/(j) = (1 · j)/(j · j) = (j)/(j^2) Step 4: Substitute j^2 = -1. (j)/(j^2) = (j)/(-1) = -j The value of -(1)/(j^7) is -j. c) Evaluate (4)/(2j^13) Step 1: Simplify the numerical part of the fraction. (4)/(2j^13) = (2)/(j^13) Step 2: Simplify the denominator j^13. j^13 = j^12 · j = (j^4)^3 · j = (1)^3 · j = 1 · j = j Step 3: Substitute the simplified denominator into the expression. (2)/(j^13) = (2)/(j) Step 4: Rationalize the denominator by multiplying the numerator and denominator by j. (2)/(j) = (2 · j)/(j · j) = (2j)/(j^2) Step 5: Substitute j^2 = -1. (2j)/(j^2) = (2j)/(-1) = -2j The value of (4)/(2j^13) is -2j.