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Chapter 2: Q35P (page 71)

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

cosh(iπ+2)

Short Answer

Expert verified

The x + iy form of the given equationcosh(iπ+2) is -3.76 .

Step by step solution

01

Given Information.

The given expression iscosh(iπ+2)i .

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 x + iy .

Use the formula cosh(x + y) = cosh xcoshy+ sinh xsinh yto break the given question.

Let us suppose.

x =2

y =π

cosh(x + y) =coshxcoshy+ sinhxsinhy

Put the values.

coshiπ+2i=cosh2cosπ+isinh(2)sinπ=-3.76

Therefore, the x + iy form of the given equationcoshiπ+2i is -3.76.

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Most popular questions from this chapter

Describe geometrically the set of points in the complex plane satisfying the following equations.|z+1|+|z-1|=8.

Show from the power series (8.1) that ez1·ez2=ez1+z2.

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

x+iy=0

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,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.

(cosπ-isinπ).

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.

3ei2x.
See all solutions

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