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Chapter 2: Q37P (page 71)

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

cos(iπ)

Short Answer

Expert verified

The x+iy form of the given equationcosiπ is 11.6.

Step by step solution

01

Given Information.

The given expression is cosiπ.

02

Meaning of rectangular form.

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

03

Write in the form of .

Let us suppose that, u=cosiπ.

It is known that, cosxi=cosh(x).

Substitute the value.

u=cosh(π)u=11.6

Therefore, the x+iyform of the given equation is, cosiπis 11.6.

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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,θin 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.

7(cos110°-isin110°).

Find the disk on convergence for each of the following complex power series.

∑n-0m(z-2+i)n2n

Test each of the following series for convergence.

∑1+in2

Express the following complex numbers in thex+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.

7.3e2(1+iπ)

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.

10.role="math" localid="1653071800850" eiπ+e-iπ
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