108. (2 109. (-1 + i)6 15
Chapter1: Equations, Inequalities, And Mathematical Modeling
Section: Chapter Questions
Problem 14PS: Proof Prove that the product of a complex number a+bi and its complex conjugate is a real number.
Related questions
Question
Question 109
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Finding a Power of a Complex Number In Exercises
107-126, use DeMoivre's Theorem to find the indicated
power of the complex number. Write the result în
standard form.
107. (1 + i)³
108. (2 + 21)6
109. (-1 + i)6
110. (3-3i)
111. 2(√3-i)s
112. 4(1-√3i)³
113. [5(cos 140° + i sin 140°)]³
114. [3(cos 150° + in 150°)]¹
115.
57 10
116.
COS
5π
4
+ i sin
TL
2 cos +
121. 3 cos
117. [2(cos + i sin 7)]¹4
118. (cos 0 + i sin 0)20
119. [4(cos 10° + i sin 10°)]6
120. [6(cos 15° + i sin 15°)]4.
#1²
i sin ¹²
71
Ft
+ i sin
each
137.
138.
139.
140.
141. C
142. F
143. C
144. C
145. Fo
146. Fo
147. Fit
148. Cu
149. Cul
150. Fou
151. Fiftl
152. Fifth
Solving a
theorem c
equation, a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F085e24e4-6db3-44bd-bedd-407e7fcd33ea%2F432ce196-b6e5-4740-b02f-78f0665fbac9%2F7meox2s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ww
Finding a Power of a Complex Number In Exercises
107-126, use DeMoivre's Theorem to find the indicated
power of the complex number. Write the result în
standard form.
107. (1 + i)³
108. (2 + 21)6
109. (-1 + i)6
110. (3-3i)
111. 2(√3-i)s
112. 4(1-√3i)³
113. [5(cos 140° + i sin 140°)]³
114. [3(cos 150° + in 150°)]¹
115.
57 10
116.
COS
5π
4
+ i sin
TL
2 cos +
121. 3 cos
117. [2(cos + i sin 7)]¹4
118. (cos 0 + i sin 0)20
119. [4(cos 10° + i sin 10°)]6
120. [6(cos 15° + i sin 15°)]4.
#1²
i sin ¹²
71
Ft
+ i sin
each
137.
138.
139.
140.
141. C
142. F
143. C
144. C
145. Fo
146. Fo
147. Fit
148. Cu
149. Cul
150. Fou
151. Fiftl
152. Fifth
Solving a
theorem c
equation, a
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