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
Morning Attitude — let's get this done. To evaluate (1+i)^-1, we first rewrite it as a fraction and then multiply the numerator and denominator by the conjugate of the denominator. Step 1: Rewrite the expression. (1+i)^-1 = (1)/(1+i) Step 2: Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of (1+i) is (1-i). (1)/(1+i) × (1-i)/(1-i) Step 3: Simplify the expression. The numerator becomes 1 × (1-i) = 1-i. The denominator is a product of a complex number and its conjugate, which simplifies to a^2 + b^2 for (a+bi)(a-bi). Here, a=1 and b=1. (1+i)(1-i) = 1^2 - i^2 = 1 - (-1) = 1+1 = 2 So the expression becomes: (1-i)/(2) Step 4: Separate into real and imaginary parts. (1)/(2) - (1)/(2)i Comparing this with the given options, it matches option (c). The final answer is (c) ((1)/(2) - (1)/(2)i). Send me the next one 📸