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Chapter 1: Q3P (page 1)

First simplify each of the following numbers to the x+iyform or to the rei胃form. Then plot the number in the complex plane.

i4

.

Short Answer

Expert verified

The complex number is 1+0i.

Step by step solution

01

Given Information

The complex number isi4 .

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=-1i4=(-12)4=(-1)42=1

Hence, the complex number is 1+0i .

The graph is mentioned below.

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Most popular questions from this chapter

Show that if p is a positive integer, thenpn=0when n>p , so (1+x)p=鈭�pnxnis just a sum ofp+1terms, from n=0 to n=p . For example,(1+x)2has 3 terms,(1+x)3 has4terms, etc. This is just the familiar binomial theorem.

Test the following series for convergence

鈭�n=0鈭�(-1)nn1+n2

Question: Test the following series for convergence

鈭�n=1鈭�(-1)n10nn+2

Derive the formula (1.4) for the sum Snof the geometric progression Sn=a+ar+ar2+.....arn-1.Hint: Multiply Snby rand subtract the result fromSn; then solve for Sn. Show that the geometric series (1.6) converges if and only if r<1; also show that if r<1, the sum is given by equation (1.8).

Show thatis the distance between the points and in the complex plane. Use this result to identify the graphs in Problems 53,54,59,and60without computation.
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