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Express the following in the form a + ib (for real a and b): 1 (a) 6+2i (b) (-+ i)¹ (c) i², i³, i4, i5,...

Express the following in the form a + ib (for real a and b): 1 (a) 6+2i (b) (-+ i)¹ (c) i², i³, i4, i5,...

Advanced Engineering Mathematics
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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The image contains three mathematical expressions that need to be rewritten in the form \(a + ib\), where \(a\) and \(b\) are real numbers. The expressions are as follows: (a) \(\frac{1}{6+2i}\) (b) \(\left(-\frac{1}{2} + i\frac{\sqrt{3}}{2}\right)^4\) (c) \(i^2, i^3, i^4, i^5, \ldots\) Each expression involves complex numbers or powers of the imaginary unit \(i\), where \(i\) is defined as \(\sqrt{-1}\). The task involves simplifying these expressions into their standard form as complex numbers.
Transcribed Image Text:The image contains three mathematical expressions that need to be rewritten in the form \(a + ib\), where \(a\) and \(b\) are real numbers. The expressions are as follows: (a) \(\frac{1}{6+2i}\) (b) \(\left(-\frac{1}{2} + i\frac{\sqrt{3}}{2}\right)^4\) (c) \(i^2, i^3, i^4, i^5, \ldots\) Each expression involves complex numbers or powers of the imaginary unit \(i\), where \(i\) is defined as \(\sqrt{-1}\). The task involves simplifying these expressions into their standard form as complex numbers.
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