MHB Solving for $z_1^*$: Argand Diagram

[fordy2707]

hi all,hope I find you all well and that I've posted this in the correct section

ive been given this $z_1$ =1-j2

Question ,find and show the result of $z_1 ^*$ on an argand diagram ,my question is what does the star symbol represent or is it a typo?

many thanks

 

[Deveno]

hi all,hope I find you all well and that I've posted this in the correct section

ive been given this $z_1$ =1-j2

Question ,find and show the result of $z_1 ^*$ on an argand diagram ,my question is what does the star symbol represent or is it a typo?

many thanks

If $j$ is meant to represent $\sqrt{-1}$, then the star most likely represents complex-conjugation, so that if:

$z = a + jb$ (with $a,b \in \Bbb R$)

then $z^{\ast} = a - jb$ (we replace the imaginary part with its negative).

 

[fordy2707]

View attachment 5669

 

[Deveno]

I don't think it's a typo-see my earlier post.

 

[fordy2707]

Yep I'm with you, thanks.i looked up the wording you used and found this to certainly be the case many thanks for the help.it amazes me that I have this thrown into my questions without any prior explanation of its meaning.

 

[HallsofIvy]

The "overline", [math]\overline{z}[/math] is more common but, yes, the asterisk is sometimes used to indicate the complex conjugate. If [math]z= x+ iy[/math], then [math]z^*= \overline{z}= x- iy[/math].