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avatar+38 

Consider the complex numbers v, w and z in the complex plane below:

[asy]
size(250);
import TrigMacros;

real big = 4;

for (int i = 1; i < big+1; ++i)
{
draw(Circle((0,0),i), lightblue + linewidth(0.4));
}

for(int i=0;i<360;i+=15) {
draw(rotate(i)*((-big,0)--(big,0)), lightblue + linewidth(0.4));
}

rr_cartesian_axes(-big,big,-big,big,complexplane=true);

pair O, V, Z, WW;

O = (0,0);
WW= 2*dir(135);
V = dir(15);
Z = 2*dir(195);

dot("$v$", V, E);
dot("$w$", WW, N);
dot("$z$", Z, S);
[/asy]
Enter the magnitudes: |v|, |w|, |z|
in that order.

 

part b: Using the same complex plane provided, find the magnitudes: |v+w|, |w+z|, |z+v| in that order

Thanks!

 Aug 13, 2024
 #1
avatar+1839 
0

For this problem, you must consider magnitude of complex numbers geometrically.

 

For the first part, the answers are |v| = 2, |w| = 3, |z| = 3.

 

For the second part, the answers are |v + w| = sqrt(2), |w + z| = 2, |z + v| = sqrt(3).

 Oct 10, 2024

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