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What is the conjugate of 
(1)/(3)-(7)/(3)i ?

-(1)/(3)-(7)/(3)i

(1)/(3)+(7)/(3)i

-(7)/(3)+(1)/(3)i

-(1)/(3)+(7)/(3)i

What is the conjugate of 1373i \frac{1}{3}-\frac{7}{3} i ?\newline1373i -\frac{1}{3}-\frac{7}{3} i \newline13+73i \frac{1}{3}+\frac{7}{3} i \newline73+13i -\frac{7}{3}+\frac{1}{3} i \newline13+73i -\frac{1}{3}+\frac{7}{3} i

Full solution

Q. What is the conjugate of 1373i \frac{1}{3}-\frac{7}{3} i ?\newline1373i -\frac{1}{3}-\frac{7}{3} i \newline13+73i \frac{1}{3}+\frac{7}{3} i \newline73+13i -\frac{7}{3}+\frac{1}{3} i \newline13+73i -\frac{1}{3}+\frac{7}{3} i
  1. Understand Conjugate Concept: Understand the concept of a conjugate. The conjugate of a complex number a+bia + bi is abia - bi, where aa and bb are real numbers. The conjugate is found by changing the sign of the imaginary part of the complex number.
  2. Identify Real and Imaginary Parts: Identify the real and imaginary parts of the given complex number.\newlineThe given complex number is (13)(73)i(\frac{1}{3}) - (\frac{7}{3})i. Here, the real part is (13)(\frac{1}{3}) and the imaginary part is (73)-(\frac{7}{3}).
  3. Apply Conjugate Concept: Apply the concept of conjugate to the given complex number.\newlineTo find the conjugate, we change the sign of the imaginary part while keeping the real part the same. Therefore, the conjugate of (13)(73)i(\frac{1}{3}) - (\frac{7}{3})i is (13)+(73)i(\frac{1}{3}) + (\frac{7}{3})i.

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