Help Please: Complex Numbers; Triangular Inequality (1 Viewer)

[Stephie-Rae]

Hey.

Now, i know that |z1 + z2| < or = |z1| + |z2| and that for equality to hold z1 and z2 have to be collinear. And i can find z1 or z2 given one of them and the modulus of the other and i can find the greatest value for |z1 +z2| obviously being when they're collinear and |z1 + z2| = |z1| + |z2| but, how do you find the lowest value of |z1 + z2|??? none of my notes or text books have anything on it, my teacher wasn't at school today and i have a test 1st period tomorrow. from all my books i only have one question which asks for the lowest value to be found, but it doesn't have worked solutions.

The question is:
If z1 = 24+7i and |z2| = 6, find the greatest and least values of |z1+z2|.

So i found the greatest value to be 31. And the answer says that the least value is 19, i just don't know how to find that.

So yeah, any help or guidance would be very much appreciated.

Steph xo

 

[azureus88]

lowest value is when they're collinear as well but the vectors are pointing in opposite directions, so in this case, its 25-6=19

 

[Stephie-Rae]

lowest value is when they're collinear as well but the vectors are pointing in opposite directions, so in this case, its 25-6=19

ohhhhh okay, that makes sense. i figured it would be something straight forward like that, that i'd be missing. okay cool, thanks heaps.

 

[tommykins]

greatest should be 25+6= 31 when they haev the same argument.

 

[Tsylana]

i think the best thing to do is to understand why they work... visualise... . or if that doesn't work... take a step down and accept xD....