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# Complex numbers subtraction help? (Further maths) Watch

1. Hi,

I am trying to work out the answer to this question

Find arg(z2-z1) when

z1 =-1+ 2i, z2 = -4 - 5i.

I would have thought that all you need to do is take -4 from -1 and -5i from 2 (ie. subtracting the real and imaginary parts) giving

z2-z1 = -3-7i

and thus use arctan(-7/-3) to get arg(z2-z1) but the answer is apparently
-1.98, not 1.17 which is the decimal answer of arctan(-7/-3)

could anyone help me out??

thanks
2. Work out the brackets like you did. Then SKETCH the point and see which angle you need. You should get the correct answer using this approach.
Hi,

I am trying to work out the answer to this question

Find arg(z2-z1) when

z1 =-1+ 2i, z2 = -4 - 5i.

I would have thought that all you need to do is take -4 from -1 and -5i from 2 (ie. subtracting the real and imaginary parts) giving

z2-z1 = -3-7i

and thus use arctan(-7/-3) to get arg(z2-z1) but the answer is apparently
-1.98, not 1.17 which is the decimal answer of arctan(-7/-3)

could anyone help me out??

thanks
Plot your new complex number and see where it lies.
Spoiler:
Show
It is in the third quadrant.

In general if , then when and . (Basically when the complex number lies in the third quadrant, but it's important to know why this works.)
Please take a look at example 4 here.

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