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3. Solve the following problems. (a) The complex number z1 = 1 - 2i is a root of the complex polynomial. p(z) = z^3 + 4z^2 + (4 + 7i)z + 15i + 5 Find all roots and factor p(z) (b) Find a polynomial p(z) of degree four with real coefficients (i.e. all coefficients are in R) which has roots ? and ? (and possible others), where ? = ?2 + i and ? = 1 + ?2i.

          3. Solve the following problems.
(a) The complex number z1 = 1 - 2i is a root of the complex polynomial.
p(z) = z^3 + 4z^2 + (4 + 7i)z + 15i + 5
Find all roots and factor p(z)
(b) Find a polynomial p(z) of degree four with real coefficients (i.e. all coefficients are in R) which has roots ? and ? (and possible others), where ? = ?2 + i and ? = 1 + ?2i.

3. Solve the following problems.
(a) The complex number z1 = 1 - 2i is a root of the complex polynomial.
p(z) = z^3 + 4z^2 + (4 + 7i)z + 15i + 5
Find all roots and factor p(z)
(b) Find a polynomial p(z) of degree four with real coefficients (i.e. all coefficients are in R) which has roots ? and ? (and possible others), where ? = ?2 + i and ? = 1 + ?2i.

Added by Melody D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Oswaldo Jiménez

Step 1

First, we are given that $z_1 = 1 - 2i$ is a root of the complex polynomial $p(z) = z^3 + 4z^2 + (4 + 7i)z + 15i + 5$. Show more…

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Solve the following problems. (a) The complex number z1 = 1 - 2i is a root of the complex polynomial. p(z) = z^3 + 4z^2 + (4 + 7i)z + 15i + 5 Find all roots and factor p(z) (b) Find a polynomial p(z) of degree four with real coefficients (i.e. all coefficients are in R) which has roots μ and λ (and possible others), where λ = √2 + i and μ = 1 + √2i.