Complete the below description of the position of these 7 complex numbers on the complex plane: The numbers are (Click for List) around the (Click for List) v of a (Click for List) with centre (Click for List) v and (Click for List) v (Click for List) v It is (Click for List) that one of the points lies on the positive real axis. (b) Sonny wants to know more about the polynomial p(z) = (z - 2)(z- z5). %3D Select ALL the statements below which are true: O The coefficients of p(z) are all purely imaginary. O The coefficients of p(z) are all complex. O The coefficients of p(z) are all real.
Complete the below description of the position of these 7 complex numbers on the complex plane: The numbers are (Click for List) around the (Click for List) v of a (Click for List) with centre (Click for List) v and (Click for List) v (Click for List) v It is (Click for List) that one of the points lies on the positive real axis. (b) Sonny wants to know more about the polynomial p(z) = (z - 2)(z- z5). %3D Select ALL the statements below which are true: O The coefficients of p(z) are all purely imaginary. O The coefficients of p(z) are all complex. O The coefficients of p(z) are all real.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
b,c please

Transcribed Image Text:(c)
Sonny's favourite polynomial happens to be
q(2) = (z – zo)*(z – z1)°(z– 2)°(z – 23)"(z – z4)°(z – 25)°(z – z6)*.
Lincoln says, "Woah! My favourite real, non-zero polynomial r(z) is divisible by q(z), and in fact it has the smallest degree possible for a polynomial with
those properties."
What is the degree of r(z)?

Transcribed Image Text:Sonny and Lincoln are amazed by the complex numbers z = 4e' (2m k/7) for k = 0,1, 2, ..., 6.
(a)
Complete the below description of the position of these 7 complex numbers on the complex plane:
The numbers are
(Click for List)
around the
(Click for List)
of a
(Click for List)
with centre
(Click for List) v
and
(Click for List) v
(Click for List)
It is
(Click for List) v
that one of the points lies on the positive real axis.
(b)
Sonny wants to know more about the polynomial p(z) = (z – 2)(z – 25).
Select ALL the statements below which are true:
O The coefficients of p(z) are all purely imaginary.
O The coefficients of p(z) are all complex.
The coefficients of p(z) are all real.
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