Q on complex number and argand diagram

[Sonal7]

Hi, I am confused as to why XB is -5 sin pi/6 +5 cos pi/6. I understand Eulers formula but I cant see the angle [MATH]\theta[/MATH] would be the angle we need. I think it should be...well i am not sure. I think it should be angle that the XB makes with the horizontal axis. I am also unsure what the bar is above XB, I think it might be a notation for vector. Never seen it like that before, I have seen arrows on top of the alphabets which indicate direction vector. Maybe its like a vector but without direction. I know complex number can be thought of like vectors.

 

[Dr.Peterson]

Hi, I am confused as to why XB is -5 sin pi/6 +5 cos pi/6. I understand Eulers formula but I cant see the angle [MATH]\theta[/MATH] would be the angle we need. I think it should be...well i am not sure. I think it should be angle that the XB makes with the horizontal axis. I am also unsure what the bar is above XB, I think it might be a notation for vector. Never seen it like that before, I have seen arrows on top of the alphabets which indicate direction vector. Maybe its like a vector but without direction. I know complex number can be thought of like vectors.

The notation (an arrow, if you look closely) does indeed represent the vector from point X to point B. It certainly does have both length and direction! But then they are representing that vector as a complex number, x + yi.

Do you not see that in -5 sin θ + 5i cos θ, θ is the angle from the vertical axis, not the horizontal? If it were the latter, they would have used 5 cos θ + 5i sin θ. This is perpendicular to that. (Don't confuse "cis" with this, which is "-sic"!)

 

[Sonal7]

The notation (an arrow, if you look closely) does indeed represent the vector from point X to point B. It certainly does have both length and direction! But then they are representing that vector as a complex number, x + yi.

Do you not see that in -5 sin θ + 5i cos θ, θ is the angle from the vertical axis, not the horizontal? If it were the latter, they would have used 5 cos θ + 5i sin θ. This is perpendicular to that. (Don't confuse "cis" with this, which is "-sic"!)

We dont know the angle from the vertical axis. We know theta that is the angle in the sector. Really confused. Good point about the cis and sic however

Sorry I get it now, AX is vertical looking at the coordinates.

 

[Sonal7]

thank you so much!