# Why am I getting Complex number results?

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Ethan Fritz on 30 Oct 2020
Commented: Ethan Fritz on 1 Nov 2020
I am doing an assignment for a course and I'm trying to map the position, velocity and acceleration of an object moving in a 2D fashion. Here is my code:
clear; clc;
rho_i=1.2;
c=6.5*10^-3;
T=300;
alpha=2.5;
theta=(45*pi)/180;
Area=pi*(.406/2)^2;
m=1225;
vi=762;
vxi=vi*cos(theta);
vyi=vi*sin(theta);
D=0.5;
g=9.81;
n=100000;
t=zeros(n,1);
x=zeros(n,1);
y=zeros(n,1);
vx=zeros(n,1);
vy=zeros(n,1);
v=zeros(n,1);
ax=zeros(n,1);
ay=zeros(n,1);
rho=zeros(n,1);
PError=zeros(8,1);
VError=zeros(8,1);
AError=zeros(8,1);
t(1)=0;
vx(1)=vxi;
vy(1)=vyi;
x(1)=0;
y(1)=0;
ax(1)=0;
ay(1)=0;
rho(1)=rho_i;
for j=1:7;
dt=10^(1-j);
for i=2:n;
t(i)=t(i-1)+dt;
vx(i)=vx(i-1)+ax(i)*t(i);
vy(i)=vy(i-1)+ay(i)*t(i);
v(i)=sqrt(vx(i)^2+vy(i)^2);
y(i)=y(i-1)+vy(i)*t(i);
x(i)=x(i-1)+vx(i)*t(i);
ax(i)=((-D*rho(i)*Area)/(2*m))*(v(i)*vx(i));
ay(i)=((-D*rho(i)*Area)/(2*m))*(v(i)*vy(i))-g;
a(i)=sqrt(ax(i)^2+ay(i)^2);
rho(i)=rho_i*(1-(c*y(i)/T)).^alpha;
end
end
I am completely confused as to why I am obtaining complex numbers for values in my arrays. Any ideas?

David Goodmanson on 31 Oct 2020
Hello Ethan,
The reason for this is that at step i = 14, the quantity on the third to last line, (1-(c*y(i)/T)) becomes negative, and since it is being taken to the alpha = 2.5 power which is not an integer power, the results are complex.
The y variables are growing far faster than they should because in several places you are using expressions such as
vx(i)=vx(i-1)+ax(i)*t(i);
rather than the correct
vx(i)=vx(i-1)+ax(i)*dt;
It's doable and not causing problems in this case, but I tend not to use i as an index variable due to possible confusion with i = sqrt(-1).

#### 1 Comment

Ethan Fritz on 1 Nov 2020
Thank you very much sir. It worked out very well. Thank you again?