Question

How do you find the complex conjugate of \[11+17i\]?

Answer 1

Hint: In this problem, we have to find the complex conjugate of the given complex number. First of all we have to write the general form of the complex number. We know that the general form of the complex number is \[z=x+iy\], where x is the real part and y is the imaginary part. We also know that the complex conjugate of z is \[\overline{z}\] and \[\overline{z}=x-iy\]. Here we just have to substitute the real and imaginary part to get the complex conjugate for the given complex number.

Complete step by step answer:
We know that the given complex number is,
\[11+17i\]……. (1)
We also know that the general form of the complex number is,
\[z=x+I y\]…….. (2)
Where, x is the real part and y is the imaginary part.
Here we can see that (1) is in the form of a complex number (2).
So, by comparing (1) and (2), we get the real part, x = 11 and the imaginary part, y = 17.
We also know that, the complex conjugate of \[z=x+iy\] is,
\[\overline{z}=x-iy\]…… (3)
Here, we can substitute the value of x and y in (3), we get
\[\overline{z}=11-17i\]
Therefore, the complex conjugate of the \[11+17i\] is \[11-17i\].

Note:
Students make mistakes when negative signs are given instead of positive in the imaginary part. When a negative sign is given, we have to conjugate it to get a positive value in the imaginary part. Students should remember that in \[z=x iy\], x is the real part, y is the imaginary part and I is the imaginary unit.