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    • Thread Starter

    I'm stuck on the second part of this question, please give me hints and clues in the right direction
    Given that z1 = 12 + 5j and z2 = -3 + 4j, verify that |z1 + z2| is less than/equal to |z1| + |z2|. I managed this part and got 12.73 < 18.
    This is the part I don't know how to do:
    Explain geometrically using an Argand diagram why |z1 + z2| is less than/equal to |z1| + |z2| is always true.
    Any help would be greatly appreciated!!

    |z1|+|z2| can only be equal to|z1+z2| If they are multiples of each other( in other words they have the same argument). If they are not multiples (have different arguments) then |z1|+|z2| is greater than |z1+z2|.
    I advise you to draw an argand diagram and draw these 2 cases and realise why this is the case.

    draw the vectors for Z1 and Z2 nose to tail... then complete the triangle; this will be vector Z1 + Z2

    Pretty sure it's an application of a triangle rule( the sum of one side is equal to or less than the sum of the other two sides)

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Updated: February 28, 2016

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