Complex graphing (1 Viewer)

[Zassaliss]

Complex numbers: the complex plane, addition and subtraction

this website states that z+1 on the argand diagram is a shift to the positive along the reals, z+2i shift to the positive on the imaginary.

Can anyone explain it to me? and explain what arg(z-2-3i)=pi/3 would look like and what z-3-3i looks like?

 

[vds700]

Complex numbers: the complex plane, addition and subtraction

this website states that z+1 on the argand diagram is a shift to the positive along the reals, z+2i shift to the positive on the imaginary.

Can anyone explain it to me? and explain what arg(z-2-3i)=pi/3 would look like and what z-3-3i looks like?

ill try explain it

z + 1: this is adding 1 the the real part of z, so z + 1 is 1 unit to the right of z

z + 2i: This is adding 2 to the imaginary part of z, so z + 2i is 2 units above z.

arg (z - 2 - 3i) = pi/3
arg [z - (2 + 3i)] = pi/3; Ok i think you put a dot 2 units to the right and 3 units up from z, then draw a ray from this, making an angle of pi/3 to the horizontal. Could someone confirm this though, im a bit rusty on the old 4 unit lol

 

[Zassaliss]

I understand what you're saying, but why is it that you have it as [z-(2+3i)]? I know to do it this way, but why?

 

[tommykins]

vectors was the reaosn i was taught iirc

 

[ronnknee]

Well think of it this way

[z-(2+3i)] is just like saying, imagine the point z on the argand diagram if it had 2 units more for the real part and 3 units more for the imaginary part ie. shifting it up by 2 units and right by 3 units