иa) Given u2 – i and v = i – 3. Expressin the form a + ib.u? + vHence, determine the modulus and argument ofu? + vb) Given a complex number z =8i.i. Express z in polar form.ii. Find all possible values of z3 and sketch them on an Argand dia-gram.c) Use De Moivre's Theorem to showcos(30) = 4 cos 0 – 3 cos 0..3COSHence, obtain all solutions of x for the following equation3x – 4x3:1.

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a) Given u = 2 – i and v = i – 3. Express in the form a + ib. u? + v Hence, determine the modulus and argument of u? + v b) Given a complex number z = - 8i. i. Express z in polar form. ii. Find all possible values of zi and sketch them on an Argand dia- gram. c) Use De Moivre's Theorem to show cos(30) = 4 cos° 0 – 3 cos 0. COS Hence, obtain all solutions of x for the following equation Зх — 423 — 1. -

a) Given u = 2 – i and v = i – 3. Express in the form a + ib. u? + v Hence, determine the modulus and argument of u? + v b) Given a complex number z = - 8i. i. Express z in polar form. ii. Find all possible values of zi and sketch them on an Argand dia- gram. c) Use De Moivre's Theorem to show cos(30) = 4 cos° 0 – 3 cos 0. COS Hence, obtain all solutions of x for the following equation Зх — 423 — 1. -

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

и
a) Given u
2 – i and v = i – 3. Express
in the form a + ib.
u? + v
Hence, determine the modulus and argument of
u? + v
b) Given a complex number z =
8i.
i. Express z in polar form.
ii. Find all possible values of z3 and sketch them on an Argand dia-
gram.
c) Use De Moivre's Theorem to show
cos(30) = 4 cos 0 – 3 cos 0.
.3
COS
Hence, obtain all solutions of x for the following equation
3x – 4x3
:1.

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