Question

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

Answer 1

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.

Answer 2

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.