SUPER EASY MATHS (好趕ga ga ga)

Modulus of 3 + 4i = root(3^2 + 4^2) = 5
Modulus of 1 - i = root(1 + 1) = root2
Modulus of -1 + i = root(1 + 1) = root2
Modulus of 6 + 8i = root(6^2 + 8^2) = 10
So

圖片參考：http://imgcld.yimg.com/8/n/HA00430051/o/701011080093113873409930.jpg

= 5^10 x (root2)^22 / [(root2)^20 x 10^8]
= 25/128

2010-11-08 18:49:41 補充：
sin-90 = -1, cos-90 = cos90 = 0
So (1/3)(0 - i) instead of (1/3)(0 + i) in the second last step.

2010-11-08 19:56:30 補充：
Before you apply the formula,you must ensure that the complex numbers are in the form
z = cosx + isinx
NOT z = cosx - isinx

For this one,

root3(cos150+isin150) / 3root3(cos240+isin240)

= (1/3)(cos90+isin-90)
= (1/3)(0+1i)
=-1/3i

is it correct??

2010-11-08 19:35:41 補充：
I want to know, why sometimes, we need to consider the angle before add or substract, but, sometimes, we do not need to consider the angle( in which quad, so it may be + or -) WHY???