2 / [ √2 - √2i] =
2 / [ √2 ( 1 - i) ] =
√2 / [ 1 - i ] =
√2 [ 1 + i ] / [ (1 - i) ( 1 + i ) ] =
√2 [ 1 + i ] / [ 1 - i^2] =
√2 [ 1 + i ] / 2 =
[ 1 + i ] / √2
1 + 1/4 = 5/4
So
(5/4) * (5/4) = 25/ 16 = 1 + 9/16
2003^1 = ends in 3
2003^2 = ends in 9
2003^3 = ends in 7
2003^4 = ends in 1 and the pattern of the ending digit repeats every 4th power
So 2003 mod 4 = 3 .........and the 3rd result in the above pattern is what we are after
So....the ending digit is 7
Add all the values
Divide by the number of them = 10
The answer will be the mean [average]
lim sin (5θ) / θ multiply top / bottom by 5
θ → 0
lim 5 * sin (5θ) /(5θ ) =
5 * lim sin (5θ) / (5θ) = ( remember........ lim sin x / x = 1 )
θ → 0 x → 0
5 * [1 ] =
5
28^(4/3) ≈ 85.02
PD = √[ (2x - 4)^2 + (2x - 9)^2 ] =
√ [ 4x^2 - 16x + 16 + 4x^2 - 36x + 81 ] =
√ [ 8x^2 - 52x + 97 ]
6.5+ (1/8)s=4.8 subtract 6.5 from both sides
(1/8) s = -1.7 multiply by 8
s = - 13.6
(4 1/2, -4 1/4), (3 3/4 , -1 1/4) =
( 9/2 , -17/4), ( 15/4 , - 5/4 ) =
(18/4 , -17/4), ( 15/4, - 5/4) midpoint =
[ ( 18/4 + 15/4)/2 , (- 17/4 + -5/4)/2 ] =
[ (33/4)/ 2 , (- 22/4)/ 2 ] =
(33/8 , - 22/8) =
(33/8 , - 11/4)
360 / 8 = 45°
360 /n = 24 → 360 / 24 = n = 15 sides
