HomeworkLib
Question

3. (10 pts) Design an algorithm how to multiply two complex numbers abi and c + di using only three multiplications of real n

engineering   Computer-Science   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

3. Algorithm to multiply two complex numbers a+bi and c+di using only three multiplications of real numbers.

Multiply-Complex-Number(a,b,c,d)
  
   1. Compute R1 = a*c = ac;
   2. Compute R2 = b*d = bd;
   3. Compute R3 = (a+b)*(c+d) = ac + ad + bc + bd
   4. Real Component = R1 - R2 = ac - bd
   5. Imaginary Component = R3 - R1 - R2
                       = (ac + ad + bc + bd) - ac - bd
                       = ad + bc
End                          

0 1
Add a comment
Know the answer?
Add Answer to:
3. (10 pts) Design an algorithm how to multiply two complex numbers abi and c + di using only three multiplications of real numbers. Your algorithm should take a, b, c and d as input and produce the...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • 1）Find the square of a complex number z=a+ib using only two real number multiplications plus as ...

    1）Find the square of a complex number z=a+ib using only two real number multiplications plus as many additions and subtractions as you wish. 2）Multiply two complex numbers z1=a+ib and z2=c+id using only 3 real number multiplications. 3）Compute (a+ib)2(c+id)2 using only 5 real number multiplications.

  • Create a class for working with complex numbers. Only 2 private float members are needed, the...

    Create a class for working with complex numbers. Only 2 private float members are needed, the real part of the complex number and the imaginary part of the complex number. The following methods should be in your class: a. A default constructor that uses default arguments in case no initializers are included in the main. b. Add two complex numbers and store the sum. c. Subtract two complex numbers and store the difference. d. Multiply two complex numbers and store...

  • 5. A complex number consists of two components: the real component and the imaginary component. A...

    C++ //add as many comments as possible 5. A complex number consists of two components: the real component and the imaginary component. An example of a complex number is 2+3i, where 2 is the real component and 3 is the imaginary component of the data. Define a class MyComplexClass. It has two data values of float type: real and imaginary This class has the following member functions A default constructor that assigns 0.0 to both its real and imaginary data...

  • USING C++, write a simple class defining complex numbers USING the FRIEND function (READ BELOW) Write...

    USING C++, write a simple class defining complex numbers USING the FRIEND function (READ BELOW) Write a C++ defining a class for complex numbers. A complex number is a number of the form: a + b ∗ i , where, for our purposes, a and b are numbers of type double, and i is a number that represents the quantity √−1. You should represent a complex number here as two values of type double. You should name the variables real...

  • JAVA PROGRAMMING A complex number is a number in the form a + bi, where a...

    JAVA PROGRAMMING A complex number is a number in the form a + bi, where a and b are real numbers and i is V-1. The numbers a and b are known as the real part and imaginary part of the complex number, respectively. You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas: a + bi + c + di = (a + c) + (b + di a + bi - (c +...

  • C++ OPTION A (Basic): Complex Numbers A complex number, c, is an ordered pair of real...

    C++ OPTION A (Basic): Complex Numbers A complex number, c, is an ordered pair of real numbers (doubles). For example, for any two real numbers, s and t, we can form the complex number: This is only part of what makes a complex number complex. Another important aspect is the definition of special rules for adding, multiplying, dividing, etc. these ordered pairs. Complex numbers are more than simply x-y coordinates because of these operations. Examples of complex numbers in this...

  • Python has the complex class for performing complex number arithmetic. For this assignment, you will design...

    Python has the complex class for performing complex number arithmetic. For this assignment, you will design and implement your own Complex class. Note that the complex class in Python is named in lowercase, while our custom Complex class is named with C in uppercase. A complex number is of the form a + bi, where a and b are real numbers and i is √-1. The numbers a and b are known as the real part and the imaginary part...

  • Complete the functions for the program complex.c (Down) . The program adds, subtracts,and multiplies complex numbers....

    Complete the functions for the program complex.c (Down) . The program adds, subtracts,and multiplies complex numbers. The C program will prompt the user for the choice of operations,read in the complex numbers, perform the operations, and print the results. The main programrepeatedly prints the menu, reads in the user’s selection, and performs the operation. We use pointers only for those arguments that the function intends to change. In all thefunctions, r represents the real component and i represents the imaginary...

  • A complex number is a number in the form a + bi, where a and b...

    A complex number is a number in the form a + bi, where a and b are real numbers and i is sqrt( -1). The numbers a and b are known as the real part and imaginary part of the complex number, respectively. You can perform addition, subtraction, multiplication, and division for complex numbers using the following formulas: a + bi + c + di = (a + c) + (b + d)i a + bi - (c + di)...

  • CODE MUST BE IN C++ Objective Create a program that provides the solution to a quadratic...

    CODE MUST BE IN C++ Objective Create a program that provides the solution to a quadratic equation. Background: A quadratic equation can be generalized by equation below: f ( x )=ax2+ bx +c Closed form solutions can be found for the zeros of a quadratic function conveniently. That is the locations where the function is equal to zero can be found by the following equation: x=− b± √ b −4ac 2a Note that depending on the sign of the expression...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT