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
To verify the statement, we will substitute the given values of a and b into the equation and check if both sides are equal. The given equation is: (2-j3) = sqrt((a+jb)) The proposed values are a=5 and b=-12. Step 1: Substitute the values of a and b into the right-hand side (RHS) of the equation. sqrt((a+jb)) = sqrt((5+j(-12))) = sqrt(5-j12) Step 2: To check if (2-j3) is equal to sqrt(5-j12), we can square both sides of the original equation. If the equality holds, then squaring both sides should also result in an equality. So, we need to check if (2-j3)^2 = 5-j12. Step 3: Calculate the square of the left-hand side (LHS), (2-j3)^2. (2-j3)^2 = 2^2 - 2(2)(j3) + (j3)^2 = 4 - j12 + j^29 Since j^2 = -1: = 4 - j12 - 9 = (4-9) - j12 = -5 - j12 Step 4: Compare the result from Step 3 with the value of a+jb. We found that (2-j3)^2 = -5 - j12. The given a+jb = 5 - j12. Comparing the two complex numbers: -5 - j12 ≠ 5 - j12 The real parts are -5 and 5, which are not equal. Therefore, the complex numbers are not equal. ❌ Incorrect. The statement (2-j3) = sqrt((a+jb)) is incorrect for a=5 and b=-12, because (2-j3)^2 = -5-j12, which is not equal to 5-j12. That's 2 down. 3 left today — send the next one.