Maths

1.
計算 P 點的極坐標：
r = √[(-3)² + (-3√3)] = 6
tanθ = (-3√3) / (-3) = √3
所以 θ = 180° + 60° = 240°

旋轉後 P 點的極坐標
= (6, 240° - 90°)
= (6, 150°)


2.
(-1 + i)³
= (-1)³ + 3(-1)²(i) + 3(-1)(i)² + (i)³
= -1 + 3i + 3 - i
= 2 + 2i


3.
設 f = 0.135353535353535353535....................
則 100f = 13.5353535353535353535....................

100f - f = 13.4
99f = 13.4
990f = 134
f = 134/990
0.135353535353535353535.................... = 67/495


4.
√[20 / 64]
= √[(2² x 5) / (2⁶)]
= (√5)/4


5.
4 / (2√5)
= 2 / √5
= 2(√5) / (√5)²
= 2(√5)/5


6.
(1)
1 + 2i
2 - 3i

(2)
6i
-2i


7.
z 為實數，則 -(3 - p)i = 0
3 - p = 0
p = 3

good!!!!!!!!!!!!!