assig12 (not to be handed in)

assig12 (not to be handed in) - = 0 can be solved as...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 135 Algebra, Assignment 12 Not to be handed in 1: Express each of the following complex numbers in cartesian form. (a) 4 e i 5 π/ 3 (b) (1 + i 3) 10 (c) 5 e i θ , where θ = tan - 1 2 2: Express each of the following complex numbers in the polar form re i θ . (a) - 2 + 2 i (b) (1 - i ) 2 (1 + i 3) (c) - 3 - i 3: Solve each of the following for z C . Express your answers in the polar form re i θ . (a) z 3 + 8 i = 0 (b) z = z - i z + 2 + i (c) z 4 = 8 z 4: For each of the following polynomials f ( x ), first solve f ( z ) = 0 for z C , and then factor f ( x ) over the real numbers. (You may find it useful to read section 9.2 in the text book). (a) f ( x ) = x 6 + 7 x 3 - 8 (b) f ( x ) = x 6 + 1 (c) f ( x ) = x 4 + 4 x 3 + 6 x 2 + 4 x + 5 5: An equation of the form ax 3 + bx 2 + cx + d = 0, where a, b, c, d C with a 6
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = 0 can be solved as follows. First, divide by a to obtain an equation of the form x 3 + Bx 2 + Cx + D = 0. Next, make the substitution x = z-B 3 . This will convert the equation to the form z 3 + pz + q = 0. Thirdly, make the substitution z = w-p 3 w . This will convert the equation to the form w 3 + r w-3 + q = 0. Finally, multiply through by w 3 to obtain w 6 + q w 3 + r = 0, which we can solve for w 3 using the Quadratic Formula. (You may nd section 9.6 useful). (a) Solve x 3-3 x + 1 = 0 for x R . (b) Solve x 3 + 3 x 2-3 x-7 = 0 for x R ....
View Full Document

Ask a homework question - tutors are online