# Using pascal's triangle and standard form

1. Sep 3, 2010

### jamster49

1. The problem statement, all variables and given/known data

If z = 4 + i and w = -2 +2i, determine (z+w)5 using Pascal’s Triangle and standard form.

2. Relevant equations

3. The attempt at a solution

2. Sep 3, 2010

### HallsofIvy

Staff Emeritus
?? (z+w)5= 5z+ 5w which has nothing to do with Pascal's triangle. Did you mean (z+ w)^i?

The first thing I would do is write z+ w= 4+i- 2+ 2i= 2- i.

so (z+ w)^5= (2- i)^5. Now, Pascal's triangle gives the coefficients for binomials of the form (a+ b)^n. In particular, the 5 th row of Pascal's triangle gives the coefficients for (a+ b)^5. Write that out, and remember that i^2= -1.