# Limit of a complex sequence

1. Nov 2, 2013

### yy205001

1. The problem statement, all variables and given/known data
a) (1+i)-n as n→∞
b) n/(1+i)n as n→∞

2. Relevant equations

3. The attempt at a solution
My answers were divergent for both question because (1+i)n=sqrt(2)*en*pi*i/4, so when n→∞, the limit is varying on the circle with radius sqrt(2). But the solution said both of them equal to 0. How can I get that?

Any help is appreciated.

2. Nov 2, 2013

### Staff: Mentor

Don't forget the minus sign, and the exponent of the magnitude.

3. Nov 2, 2013

### yy205001

mfb:
But when the minus is there, the value is still varying, it does not go to infinity in denominator for part a. So I still cannot get the limit equal to 0.

4. Nov 2, 2013

### HallsofIvy

Staff Emeritus
There's your error $(re^{i\theta})^n= r^n e^{ni\theta}$. $(1+ i)^n= (\sqrt{2})^n e^{n\pi i/4}$. You did not take the absolute value to the -n powerr.

5. Nov 2, 2013

### yy205001

Hallsoflvy:
oh yeah! So sqrt(2)-n→0 as n→∞!?

6. Nov 2, 2013

### HallsofIvy

Staff Emeritus
Yes.

7. Nov 2, 2013

### yy205001

Thank you so much!

8. Nov 2, 2013

### Staff: Mentor

That's what I meant with "the exponent of the magnitude.".