+38 Consider the complex numbers and in the complex plane below:
[asy]
size(250);
import TrigMacros;
real big = 5;
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 V, Z, WW;
V= (sqrt(2)/2, sqrt(2)/2);
WW = (2*sqrt(2), 2*sqrt(2));
Z = (0, -3);
dot("$v$", V, N);
dot("$w$", WW, N);
dot("$z$", Z, E);
[/asy]
a)If we have that v=r1e^iθ1, w=r2e^iθ2, z=r3e^iθ3, for positive r1, r2 and r3 and for θ1, θ2 and θ3 between 0 and 2pi, enter r1, θ1, r2, θ2, r3, θ3 in that order
b)Consider the complex numbers in the complex plane below:
[asy]
size(250);
import TrigMacros;
real big = 5;
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 V, Z, WW;
V= (sqrt(2), -sqrt(2));
WW = 2(sqrt(3), 1)*dir(-15);
Z = (-3,0);
dot("$v$", V, N);
dot("$w$", WW, N);
dot("$z$", Z, S);
[/asy]
If the conjugates of these complex numbers satisfy conj(v)=r1e^iθ1, conj(w)=r2e^iθ2, conj(z)=r3e^iθ3, for positive r1, r2 and r3 and for θ1, θ2 and θ3 between 0 and 2pi, enter r1, θ1, r2, θ2, r3, θ3 in that order
Thanks!
