153k views
5 votes
Complete the indicated operations with complex numbers z1=(3-i and z2=-i. Match each operation with the correct answer. 1. z1*z2 2. z1/z2 3. z1+z2 4. z1-z2 a. -1-i√3 b. 1+i√3 c. √3-2i d. √3

User Niveathika
by
8.4k points

2 Answers

2 votes

Final answer:

To find the results of the indicated operations with complex numbers z1=(3-i) and z2=-i, we multiply z1 and z2 to get i, divide z1 by z2 to get 1+3i, add z1 and z2 to get 2-i, and subtract z2 from z1 to get 3+i.

Step-by-step explanation:

To complete the indicated operations with complex numbers, we will use the given values of z1=3-i and z2=-i.

  1. To multiply z1 and z2, we multiply their real and imaginary parts separately. Multiplying (3)(0) and (-1)(-1), we get a real part of 0 and an imaginary part of 1. So z1*z2 = 0 + i = i.
  2. To divide z1 by z2, we multiply both the numerator and denominator by the complex conjugate of z2. The complex conjugate of -i is -i itself. So, (3-i)/(-i) = ((3-i)(-i))/((-i)(-i)) = (-3i+i²)/(i²) = (-3i-1)/(-1) = 3i+1 = 1+3i.
  3. To add z1 and z2, we add their real parts and imaginary parts separately. Adding 3 and 0, we get a real part of 3. Adding -1 and -i, we get an imaginary part of -1-i. So z1+z2 = 3 + (-1-i) = 2-i.
  4. To subtract z2 from z1, we subtract their real parts and imaginary parts separately. Subtracting -1 from 3, we get a real part of 4. Subtracting -i from -1, we get an imaginary part of -1+i. So z1-z2 = 4 + (-1+i) = 3+i.
User Khaled Alam
by
8.0k points
0 votes

Final answer:

To complete the indicated operations with complex numbers z1=(3-i) and z2=-i, the answers are: 1. z1 * z2 = 1, 2. z1 / z2 = -1 + 3i, 3. z1 + z2 = 3, 4. z1 - z2 = 3.

Step-by-step explanation:

To complete the indicated operations with complex numbers z1=(3-i) and z2=-i, we can use the properties of complex numbers.

  1. To find z1 * z2, we multiply the real parts and the imaginary parts separately. (3 * 0) - (1 * -1) = 0 - (-1) = 1. So, the answer is 1.
  2. To find z1 / z2, we multiply z1 by the complex conjugate of z2, which is just -i. (3 - i) * (-i) = 3i + i^2 = 3i - 1 = -1 + 3i. So, the answer is -1 + 3i.
  3. To find z1 + z2, we add the real parts and the imaginary parts separately. 3 + 0 = 3. So, the answer is 3.
  4. To find z1 - z2, we subtract the real parts and the imaginary parts separately. 3 - 0 = 3. So, the answer is 3.
User Nungster
by
7.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories