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    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
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    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.
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    (Original post by SWIMSHALLOW)
    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 z = x + yi, then \arg z = - \left \{ \pi - \arctan\left ( \frac{y}{x} \right ) \right \} when x < 0 and  y < 0. (Basically when the complex number z 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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     \text{arg}(z) = \arctan{ \bigg( \dfrac{\text{Im}}{\text{Re}} \bigg)}
 
 
 
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