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Chapter 2: Q32P (page 71)

Find each of the following in the x + iyform and check your answers by computer.

cosh(iπ2-ln3)

Short Answer

Expert verified

The form of the given equation coshiπ2-ln3is-4i3.

Step by step solution

01

Given Information.

The given expression is iπ2-ln3.

02

Meaning of rectangular form.

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

03

Write in the form of .

Use the formula cosh(x+y)=coshxcoshy+sinhxsinhyto break the given question.

Consider the following values.

role="math" localid="1658811061300" x=-ln3y=π2cosh(x+y)=coshxcoshy+sinhxsinhy

Put the values.

coshiπ2-ln3=cosh(-ln3)cosπ2+isinh(-ln3)sinhπ2

Therefore, the x + iy form of the given equation coshiπ2-ln3is-4i3.

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Most popular questions from this chapter


Express the following complex numbers in the x+iy form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

22.1−i242

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,θ 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.

5(cos20°+isin20°).

Express the following complex numbers in the x+iyform. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.

16.(i−3)(1+i3)

Solve for all possible values of the real numbers xand yin the following equations.

x+iy=0

Question:First simplify each of the following numbers to the x+iyform or to thereiθform. Then plot the number in the complex plane.

10.5(cos40°+isin40°.
See all solutions

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