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AME525_Homework_10_Solutions_111407

# AME525_Homework_10_Solutions_111407 - W/O Sail/ms Section...

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Unformatted text preview: W /O Sail/ms Section 20.1 Complex Numbers 4 (2+i)—(3—4i)~_(—1+5i)(16—27Z) —6+822‘_—3+412‘ ' (5-72)(3+z') "(16+2i)(16—2i)” 260 ” 130 8. (3 + i)3 = 27+ 3(3)2i + 3(3)(2‘)2 +713 = 27+277l —‘ 9 —i = 18 + 26¢ 12. With 2 = a + 62322 = (a2 — ()2) + 2abi, so Re(22) = a2 — b2 and Im(22) = 2ab. . 3- 18. arg(—2 + 22) = I” + 27rk, k any integer. 24. We have I — 77lI = 7, and an argument is 0 = —12r-,_ so polar form is 7e‘iW/2_ . 1 . 26. We have I — 4 — zI = x/ﬁﬂ = Tan-1(a) +7r is one argument, so polar form is meﬁTan‘Rwa) 28. We have I — 12 + 3iI == v153,0 = Tan‘1 (—i) + 1r is an argument, so polar form is 153ei(Tan‘1(—%)+7r) ...
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