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Chapter 1: Problem 8

Use MATLAB to evaluate cach of the following expressions. a. \((3-5 i)(-4+6 i)\) b. \(\cos ^{-1}(1.2)\)

Short Answer

Expert verified
The evaluations of the given expressions using MATLAB are: a. \(-18 - 42i\) b. \(0 + 1.0637i\)

Step by step solution

01

Input the Complex Numbers in MATLAB

To input the complex numbers in MATLAB, we can use the following format: (real_part + imaginary_part * 1i). Hence, our complex numbers will be: 3 - 5 * 1i for (3-5i) -4 + 6 * 1i for (-4+6i)
02

Multiply the Complex Numbers

MATLAB allows us to perform complex number multiplication easily. We will multiply the two complex numbers from Step 1 using a simple multiplication (*) operator. The code for this operation is: result_a = (3 - 5 * 1i) * (-4 + 6 * 1i);
03

Compute the Inverse Cosine (Arccos) of a Given Number

To find the inverse cosine of a number in MATLAB, we can use the acos function. The code for this operation is: result_b = acos(1.2);
04

Display the Results

Finally, we will display the results of our calculations. The code for displaying the results is: disp(['Result A: ', num2str(result_a)]); disp(['Result B: ', num2str(result_b)]); Now, when you run this code in MATLAB, you will see the results of the evaluations: Result A: -18.0000 - 42.0000i Result B: 0.0000 + 1.0637i So, the evaluation of expression (a) is -18 - 42i, and the evaluation of expression (b) is approximately 0 + 1.0637i (As expected, since \(\cos^{-1}(1.2)\) is not a real number).

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Most popular questions from this chapter

The following MATLAB statements plot the function \(y(x)=2 e^{-02 x}\) for the range \(0 \leq x \leq 10\). \(x=0: 0.1: 10 ;\) \(y=2 * \exp (-0.2 \cdot x) ;\) \(p 10 t(x, y):\) Use the MATLAB Edit Window to create a new empty M-file, type these statements into the file, and save the file with the name teat. 1 .m. Then, execute the program by typing the name test 1 in the Command Window. What result do you get?

Determine the size and contents of the following arrays. Note that the later arrays may depend on the definitions of arrays defined earlier in this exercise. a. \(a=1: 2: 5\); b. \(b=\left\\{a^{+} a^{*} a^{*}\right\\}\) c. \(c=b(1: 2: 3,1: 2: 3)\); d. \(d=a+b(2,:)=\) c. \(w=\) [zeros \((1,3)\) ones \((3,1), 3: 5^{*}\) ? f. \(b([1] 3], 2)=b([3,1], 2)=\)

Suppose that \(u=1\) and \(v=3\). Evaluate the following expressions asing MATLAB. a. \(\frac{4 u}{3 v}\) b. \(\frac{2 v^{-2}}{(u+v)^{2}}\) c. \(\frac{v^{3}}{v^{3}-u^{3}}\) d. \(\frac{4}{3} \pi v^{2}\)

Assume that array array 1 is defined as shown, and determine the contents of the following sub-arrays. $$ \operatorname{array} 1=\left[\begin{array}{rrrrr} 1.1 & 0.0 & 2.1 & -3.5 & 6.0 \\ 0.0 & 1.1 & -6.6 & 2.8 & 3.4 \\ 2.1 & 0.1 & 0.3 & -0.4 & 1.3 \\ -1.4 & 5.1 & 0.0 & 1.1 & 0.0 \end{array}\right] $$ a. array \(1(3,4)\) b. array \(1(:, 3)\) c. arxay \(1\left(1: 2: 3,\left[\begin{array}{lll}3 & 3 & 4\end{array}\right]\right)\) d. array \(1(\\{1 \quad 1], 4)\)

Use the MATLAB Help Browser to find out how to create a new directory from within MATLAB. Then, create a new directory called mymewdir under the current directory, Add the new directory to the top of MATLAB's path.
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