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Chapter 2: Q1MP (page 80)

Find one or more values of each of the following complex expressions and compare with a computer solution.

(1+i1-i)2718

Short Answer

Expert verified

The value of the complex number is,z=-1 .

Step by step solution

01

Given Information.

The given expression is,(1+i1-i)2718 .

02

Definition of complex series.

The numbers that are presented in the form ofa+ib where, a is real numbers and ' ib ' is an imaginary number called complex numbers.

Example:3+2i .

03

Convert into polar form.

Consider.

z1=1+iz2=1-i

Write both in polar form.

z1=1+iz1=2e蟺颈/4z2=1-iz2=2e-蟺颈/4

04

Substitute the values and solve.

Put both the value in the given question.

z=1+i1-i2718z=2e蟺颈/42e-蟺颈/42718z=e蟺颈/42718z=e1359蟺颈

z=cos(1359蟺)+isin(1359蟺)z=cos(1359蟺-2苍蟺)+isin(1359蟺-2苍蟺)z=cos(1359蟺-1358蟺)+isin(1359蟺-1358蟺)z=cos蟺+isin蟺

z=-1

Hence the value is found to be1+i1-i2718=-1

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Most popular questions from this chapter

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly findx,y,r,胃in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

2(cos蟺6+isin蟺6).

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

2+3i1-i.

Solve for all possible values of the real numbersand in the following equations.

2ix+3=y-i

Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.

253+4i.

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find x,y,r,胃in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

4(cos2蟺3+isin2蟺3).
See all solutions

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