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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(颈蟺2-ln3)

Short Answer

Expert verified

The form of the given equation coshi蟺2-ln3is-4i3.

Step by step solution

01

Given Information.

The given expression is i蟺2-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=蟺2cosh(x+y)=coshxcoshy+sinhxsinhy

Put the values.

coshi蟺2-ln3=cosh(-ln3)cos蟺2+isinh(-ln3)sinh蟺2

Therefore, the x + iy form of the given equation coshi蟺2-ln3is-4i3.

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Most popular questions from this chapter

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

3(cos28掳+isin28掳).

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.

12.4e-8i蟺/3

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

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

|z+3i|=4.

Test each of the following series for convergence.

鈭�1/(1+i)n
See all solutions

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