A. Simplify5 / j^10 and (3-2j)(1-3j) in the form of a + bj.
B. If a =5i + 3j and b = 3i – 2j, find: 1. a + b; 2. themodulus of a + b.
C. If a =2i – j +3k and b = i + 2j – 2k, find a x b.Please show few steps..
Complex Number!!!
2011-03-09 8:12 am
回答 (1)
2011-03-09 11:21 am
✔ 最佳答案
A. 5/j^10 = 5/(j^2)^5 = 5/[(-1)^5] = 5/(-1) = -5(3-2j)(1-3j) = 3 - 2j -9 +6j^2 =3 - 2j -9 +6(-1) = -12 - 2j
B1. Assume a, b are vectors
a+b = (5+3) i +(3-2)j =8i+j
B2. By Pyth. Theorem,
|a+b| = √(8^2 + 1^2) =√65
C. Assume a,b are vectors and x being cross product
axb
| i j k |
= | 2 -1 3 |
| 1 2 -2|
= + [(-1)(-2) - (3)(2)] i - [(2)(-2)-(3)(1)] j + [(2)(2)-(-1)(1)] k
= -4 i +7 j +5k
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