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Chapter 2: Q2P (page 74)

Evaluate each of the following in x+iyform, and compare with a computer solution.

ln(-i)

Short Answer

Expert verified

Thex+iy form of the given equationln(-i) is3蟺2i .

Step by step solution

01

Given Information.

The given expression isln(-i) .

02

Meaning of rectangular form.

Represent the complex number in rectangular form means writing the given complex number in the form ofx+iy in which x is the real part and y is the imaginary part.

03

Convert in polar form.

Consider, z=-i.

Write the polar form of the number.

z=rei胃

The angle is located in negative imaginary axis so the angle must be accordingly.

r=-ir=1胃=3蟺2

Put the values in the polar form.

z=e3蟺2i

04

Write in the form of x+iy .

Convert the polar form into the rectangular form.

z=re胃ilnz=ln(r)+lne胃iln(-i)=ln(1)+3蟺2ilne

Therefore,x+iythe form of the given equation (-i)is 3蟺2i.

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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 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).

Test each of the following series for convergence.

鈭�(1+i)n

Question: 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.

5-2i5+2i.

Follow steps (a), (b), (c) above to find all the values of the indicated roots -13.

Solve for all possible values of the real numbers xand yin the following equations. (2x-3y-5)+i(x+2y+1)=0
See all solutions

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