TM UTM a) Given two complex numbers z = 2+ 3i and w= UTM i. Find zw in a + bi form and in polar form. ii. Find the polar for UTM TM UTM for zw TM UTM 1-2i UTM UTM UTM SU

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.3: Polar Form Of Complex Numbers; De Moivre's Theorem
Problem 3E
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QUESTION
TM
a) Given two complex numbers a
TM UTM
i. Find zw in a +bi form and in polar form.
form UTM
for
UTM UTM
2= = 2+ 3i and w=
ii. Find the polar
zw
Hence,
UTM
Find all the cube roots for the equation 23 +8i = 0. Hence, deduce all the cube
roots for (2z-1)³ +8i = 0,0
UTM
UTM
TM UTM UTM
2i
c) Use De Moivro's theorem and binomial theorem or otherwise to show that
TM UTM
HTM
cos(30) = 4 cos³ 0-3 cos. UTM
TM
UTMUTM
UTM UTM UTM
TM UTM btain all possible solutions to the e
- 9 cos 0 + 1 = 0.
UTMUT quation
UTM UTM UTM
Transcribed Image Text:QUESTION TM a) Given two complex numbers a TM UTM i. Find zw in a +bi form and in polar form. form UTM for UTM UTM 2= = 2+ 3i and w= ii. Find the polar zw Hence, UTM Find all the cube roots for the equation 23 +8i = 0. Hence, deduce all the cube roots for (2z-1)³ +8i = 0,0 UTM UTM TM UTM UTM 2i c) Use De Moivro's theorem and binomial theorem or otherwise to show that TM UTM HTM cos(30) = 4 cos³ 0-3 cos. UTM TM UTMUTM UTM UTM UTM TM UTM btain all possible solutions to the e - 9 cos 0 + 1 = 0. UTMUT quation UTM UTM UTM
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