Find \(\left|\left(\frac 35+\frac 45i\right)^6\right|\)
Multiplying this out the long way is tedious, put will give you the correct answer.
You can use the shortcut: (x + y)6 = x6 + 6x5y + 15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + y6
where x = 3/5 and y = 4/5·i. (You can get the coefficients by using either combinations, or Pascal's triangle.)
Finally, find the absolute value of the answer.