EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780135795910
Author: Demana
Publisher: PEARSON CO
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Expert Solution & Answer
Chapter 6, Problem 38RE
Solution
To find: the
The standard form of the complex number 4(cos2.5+isin2.5) is approximately −3.20+2.39i .
Given information:
Given polar form of complex number is 4(cos2.5+isin2.5) .
Formula used:
- Polar form to Standard form of complex number:
- cos(2.5)≈−0.80, sin(2.5)≈0.598 .
If polar form a complex number z is r(cosθ+isinθ) , then standard form of z is a+bi , where a=rcosθ, b=rsinθ, and r=√a2+b2 .
Calculation:
Compare given complex number 4(cos2.5+isin2.5) with polar form r(cosθ+isinθ). Conclude that r=4, and θ=2.5 .
Standard form of complex number:
The standard form of 4(cos2.5+isin2.5) is a+bi . The values of a and b
computed as follows:
Substitute the values of r and θ in the equations a=rcosθ and b=rsinθ:
a=rcosθ=4(cos2.5)≈4(−0.80)=−3.20
b=rsinθ=4(sin2.5)≈4(0.598)≈2.39
Thus, the standard form of the complex number 4(cos2.5+isin2.5) is approximately −3.20+2.39i .
Chapter 6 Solutions
EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
Ch. 6.1 - Prob. 1QRCh. 6.1 - Prob. 2QRCh. 6.1 - Prob. 3QRCh. 6.1 - Prob. 4QRCh. 6.1 - Prob. 5QRCh. 6.1 - Prob. 6QRCh. 6.1 - Prob. 7QRCh. 6.1 - Prob. 8QRCh. 6.1 - Prob. 9QRCh. 6.1 - Prob. 10QR
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