Question

How do you find the complex conjugate \[3-7i\] ?

Answer 1

Hint: In the above question we have to find conjugate \[3-7i\] . In order to find we have to just change the sign of the imaginary part of the complex conjugate. There is no change in the real part. Thus, in the given complex number we will change the sign of the imaginary part which is \[-7i\] .

Complete step by step answer:
The concept involved in the above question is of trigonometric form of complex numbers and conjugate of a complex number. A complex number has two parts one is teal and the other one is imaginary. The imaginary part is represented by \[i=\sqrt{-1}\] , iota as no real number satisfies this equation. iota is called the imaginary number. When each of the two complex numbers have the same real part and equal value of the imaginary part but of opposite signs then they both are said to be conjugate of each other.
Let us take an example before solving the question. If we have a complex number, suppose \[a+ib\] , here is the real part and \[ib\] as the imaginary part. if we want to write its conjugate part then we have to change the sign of the imaginary part without touching the real part. So, the conjugate of the complex number is \[a-ib\] .
Now coming to the question, the given complex number is \[3-7i\] .
The conjugate for the above complex number is \[3+7i\] .
Hence the answer to the above question is \[3+7i\] .

Note:While solving the above question keep in mind the basic definition of conjugate of a complex number. Do not forget to mention the iota with the imaginary part. Remember that in a conjugate part the real number doesn’t change.