Complex Numbers

1. (2 + √-2)(3 + √-2)
= 2(3 + √-2) + √-2(3 + √-2)
= 6 + 2√-2 + 3√-2 – 2
= 4 + 5√-2 or 4 + 5√2 i
2. (2 – 5√2 i)(3 + 4√2 i)
= 2(3 + 4√2 i) – 5√2 i(3 + 4√2 i)
= 6 + 8√2 i – 15√2 i – 20(2) i2
= 6 – 7√2 i + 40
= 46 – 7√2 i
3. (4 – √-2)(4 + √-2)
= 42 – (√-2)2
= 16 – (-2)
= 18
4. (√-5 + 1)2
= (√-5)2 + 2(√-5) + 1
= -5 + 2√-5 + 1
= -4 + 2√5 i
5.(-3 – 2√-2)2
= (-3)2 – 2(-3)(2√-2) + (2√-2)2
= 9 +12√-2 – 8
= 1 + 12√2 i

2009-08-13 23:24:32 補充：
5.(-3 – 2√-2)^2
= (-3)^2 – 2(-3)(2√-2) + (2√-2)^2
= 9 +12√-2 – 8
= 1 + 12√2 i