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Chapter 2: Q36P (page 71)

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

sinh(1+i蟺2)

Short Answer

Expert verified

The x + iy form of the given equationsinh(1+颈蟺2) is 1.543 i .

Step by step solution

01

Given Information.

The given expression is sinh(1+颈蟺2).

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 sinh(x + y) = sinh xh cos y+cosh xsinh yto break the given question.

Consider the following values.

x=1y=蟺2

sinh(x + yi) = sinh (x)cos(y)+ icosh(x)sinh(y)

Put the value.

sinh1+i蟺2=sinh(1)cos蟺2+icosh(1)sin蟺2=1.543i

Therefore, the x + iy form of the given equationsinh1+i蟺2 is 1.543 i.

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Most popular questions from this chapter

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

Re(z)>2.

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)

Test each of the following series for convergence.

鈭�(1+i)n

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鈥攖ry 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.

13.(i鈭�3)31鈭�i

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