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What is the conjugate of 
(1)/(4)-(5)/(4)i ?

-(1)/(4)-(5)/(4)i

-(5)/(4)+(1)/(4)i

-(1)/(4)+(5)/(4)i

(1)/(4)+(5)/(4)i

What is the conjugate of 1454i \frac{1}{4}-\frac{5}{4} i ?\newline1454i -\frac{1}{4}-\frac{5}{4} i \newline54+14i -\frac{5}{4}+\frac{1}{4} i \newline14+54i -\frac{1}{4}+\frac{5}{4} i \newline14+54i \frac{1}{4}+\frac{5}{4} i

Full solution

Q. What is the conjugate of 1454i \frac{1}{4}-\frac{5}{4} i ?\newline1454i -\frac{1}{4}-\frac{5}{4} i \newline54+14i -\frac{5}{4}+\frac{1}{4} i \newline14+54i -\frac{1}{4}+\frac{5}{4} i \newline14+54i \frac{1}{4}+\frac{5}{4} i
  1. Find Conjugate: The conjugate of a complex number a+bia + bi is abia - bi. To find the conjugate, we simply change the sign of the imaginary part.
  2. Given Complex Number: Given the complex number (14)(54)i(\frac{1}{4}) - (\frac{5}{4})i, the conjugate will be (14)+(54)i(\frac{1}{4}) + (\frac{5}{4})i, because we change the sign of the imaginary part from negative to positive.
  3. Check Options: Check the given options to find the correct conjugate.
  4. Correct Conjugate: The correct conjugate of (14)(54)i(\frac{1}{4}) - (\frac{5}{4})i is (14)+(54)i(\frac{1}{4}) + (\frac{5}{4})i, which matches one of the given options.

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