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Chapter 2: Q7MP (page 80)

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

(-i)'

Short Answer

Expert verified

The value of -i'is,e-蟺2卤2n蟺 .

Step by step solution

01

Given Information

The given expression is,-i' .

02

Definition of Complex Numbers

The numbers that are presented in the form of x+iywhere, 'x' is real numbers and 'iy' is an imaginary number, those numbers are referred to as called Complex numbers.

03

 Use the logarithmic functions to obtain the result

Consider,w=-i' .

Write the number in the form, w=eiIn-i. 鈥�. (1)

Use logarithmic functions to find the value of In-i .

In-i=Inr+i胃卤2n蟺n=0,1,2,3,.....

=In1+i蟺2卤2n蟺=i蟺2卤2n蟺........2

Put the value of In -iin equation (1).

w=ei.i蟺2卤2n蟺w=e-蟺2卤2n蟺n=0,1,2,3,.......

Hence the value of -iiis, e-蟺2卤2n蟺.

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Most popular questions from this chapter

Find each of the following in rectangular a+zb form if z=2-z3; if z=x+zy.

1z-1

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.

role="math" localid="1658476746206" (cos3蟺2+isin3蟺2)

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

2.8e-i(1.1).

Describe geometrically the set of points in the complex plane satisfying the following equations.

Re(z2)=4.

Solve for all possible values of the real numbers xand y in the following equations x+iyx-iy=-i.

See all solutions

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