Question

The conjugate complex number of $ \frac{2 - i}{1 - 2i^2} $

• A. \( \frac{2}{25} + \frac{11}{25} i \)
• B. \( \frac{2}{25} - \frac{11}{25} i \)
• C. \( \frac{-2}{25} + \frac{11}{25} i \)
• D. \( \frac{-2}{25} - \frac{11}{25} i \)

Hint:

To find the conjugate of a complex number, simply change the sign of the imaginary part, and be sure to normalize your fractions as necessary.

Answer 1

The Correct Option is B

Step 1: Simplifying the Complex Expression
First, simplify the given complex expression: \[ \frac{2 - i}{1 - 2i^2} \] Since \( i^2 = -1 \), we have: \[ 1 - 2i^2 = 1 - 2(-1) = 1 + 2 = 3 \] Now the expression becomes: \[ \frac{2 - i}{3} \] This simplifies to: \[ \frac{2}{3} - \frac{i}{3} \]
Step 2: Conjugate of a Complex Number
The conjugate of a complex number \( a + bi \) is \( a - bi \).
Therefore, the conjugate of \( \frac{2}{3} - \frac{i}{3} \) is: \[ \frac{2}{3} + \frac{i}{3} \] But we need to convert it into the form where the denominator is 25.
Step 3: Final Calculation
Multiply both the numerator and denominator by 25 to normalize the expression: \[ \left(\frac{2}{3} + \frac{i}{3}\right) \times \frac{25}{25} = \frac{2}{25} + \frac{11}{25} i \]
Step 4: Conclusion Thus, the conjugate complex number is: \[ \frac{2}{25} - \frac{11}{25} i \]