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Chapter 1: Q4P (page 1)

First simplify each of the following numbers to the x+iy form or to the reiθ form. Then plot the number in the complex plane.

i2+2i+1

Short Answer

Expert verified

Factorize the complex number.

i=-1i2+2i+1=(-1)2+2i+1=-1+2i+1=2i

The complex number is 0+2i.

Step by step solution

01

Given Information

The complex number isi2+2i+1 .

02

Definition of the Complex number

A complex number is a number that is made up of both real and imaginary numbers.

03

Find the value

Factorize the complex number.

i=-1i2+2i+1=(-1)2+2i+1=-1+2i+1=2i

Hence, the complex number is 0+2i .

The graph is mentioned below.

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Most popular questions from this chapter

By computer or tables, find the exact sum of each of the following series.

(a)∑n=1∞n(4n2-1)2(b)∑n=1∞n3n!(c)∑n=1∞n(n+1)3n

Find the interval of convergence of each of the following power series; be sure to investigate the endpoints of the interval in each case ∑n=1∞(-1)nxnn(n+1).

1-x1+x

Find the sum of each of the following series by recognizing it as the Maclaurin series for a function evaluated at a point.

∑n=0∞(-1)n(2n)!(π2)2n

The velocityof electrons from a high energy accelerator is very near the velocityof light. Given the voltage Vof the accelerator, we often want to calculate the ratio v / c. The relativistic formula for this calculation is (approximately, forV≫1)

vc=1-(0.511V)2, V=Number of million volts

Use two terms of the binomial series (13.5) to find1 - v/cin terms ofV. Use your result to find 1 - v/cfor the following values of V. Caution: V= the number of millionvolts.

(a) V =100 million volts

(b)V =500 million volts

(c)V =25,000 million volts

(d)V =100 gigavolts (100109 volts105 million volts)
See all solutions

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