Verify if (2-j3) = sqrt((a+jb)) with a=5 and b=−12.

Question

ScanSolve AI Tutor · Accepted 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) = √((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. √((a+jb)) = √((5+j(−12))) = √(5−j12) Step 2: To check if (2−j3) is equal to √(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 = 2² − 2(2)(j3) + (j3)²; = 4 − j12 + j²⁹; Since j² = −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) = √((a+jb)) is incorrect for a=5 and b=−12, because (2−j3)² = −5−j12, which is not equal to 5−j12.

Verify if (2−j3) = sqrt((a+jb)) with a=5 and b=-12.

Answer

Step-by-step solution

Substitute the values of $a$ and $b$ into the right-hand side (RHS) of the equation.

To check if $(2-j3)$ is equal to $\sqrt{5-j12}$ , we can square both sides of the original equation.

Calculate the square of the left-hand side (LHS), $(2-j3)^2$ .

Compare the result from Step 3 with the value of $a+jb$ .

Still stuck on this one?

More Mathematics Questions

Verify if (2−j3) = sqrt((a+jb)) with a=5 and b=-12.

Answer

Step-by-step solution

Substitute the values of aaa and bbb into the right-hand side (RHS) of the equation.

To check if (2−j3)(2-j3)(2−j3) is equal to 5−j12\sqrt{5-j12}5−j12​, we can square both sides of the original equation.

Calculate the square of the left-hand side (LHS), (2−j3)2(2-j3)^2(2−j3)2.

Compare the result from Step 3 with the value of a+jba+jba+jb.