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Unformatted text preview: Diﬀerential Equations
Homework Assignment 4
Due on Thursday, February 17, at the start of the recitation you are registered in
Your homework should have a cover sheet with the following information: course title,
recitation, last and ﬁrst name (as they appear in the roster), number of homework. If you
use several sheets, please staple them. The problems should be written neatly and in the
order they were assigned.
Problem 1. Find Re √3+2i and Im 52i i .
− Problem 2. (a) Write the two polar forms of √ 3 + i. (b) Write eiπ/4 , eiπ/2 and e3iπ is the form a + ib, where a and b are real.
Problem 3. Solve the equations.
(a) z 2 + 2z + 4 = 0,
(b) z 2 − z + 13 = 0.
Problem 4. Solve the system x1 +2x2 +3x3 +5x4 = 2, 2x +4x2 +8x3 +12x4 = 6,
1 3x1 +6x2 +7x3 +13x4 = 4.
Problem 5. Solve the system 3x1
−6x3 +6x4 +4x5 = −5,
−7x2 +8x3 −5x4 +8x5 = 9,
−9x2 +12x3 −9x4 +6x5 = 15. ...
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