Z1=(8-7i) z2=(-4+7i)

To work with complex numbers, we can perform different operations such as addition, subtraction, multiplication, and division. Let's perform these operations with the given complex numbers z1 and z2.

Addition (z1 + z2):

z1 + z2 = (8 - 7i) + (-4 + 7i)

To add complex numbers, we simply add their real and imaginary parts separately.

Real part: 8 + (-4) = 4 Imaginary part: (-7i) + (7i) = 0

Therefore, z1 + z2 = 4 + 0i = 4

Subtraction (z1 - z2):

z1 - z2 = (8 - 7i) - (-4 + 7i)

Similar to addition, we subtract the real and imaginary parts separately.

Real part: 8 - (-4) = 12 Imaginary part: (-7i) - (7i) = -14i

Therefore, z1 - z2 = 12 - 14i

Multiplication (z1 * z2):

z1 * z2 = (8 - 7i) * (-4 + 7i)

To multiply complex numbers, we can use the FOIL method.

(8)(-4) = -32 (Real part) (8)(7i) = 56i (Imaginary part) (-7i)(-4) = 28i (Imaginary part) (-7i)(7i) = -49 (Real part, since i^2 = -1)

Combining the real and imaginary parts:

Real part: -32 + (-49) = -81 Imaginary part: 56i + 28i = 84i

Therefore, z1 * z2 = -81 + 84i

Division (z1 / z2):

To divide complex numbers, we can use the conjugate of the denominator to eliminate the imaginary part.

z1 / z2 = (8 - 7i) / (-4 + 7i)

Multiply the numerator and denominator by the conjugate of the denominator (-4 - 7i).

[(8 - 7i) * (-4 - 7i)] / [(-4 + 7i) * (-4 - 7i)]

Expanding the numerator and denominator:

[(8 * -4) + (8 * -7i) + (-7i * -4) + (-7i * -7i)] / [(16 + 28i - 28i - 49)]

Simplifying:

[-32 - 56i - 28i - 49] / [-33]

Combining like terms:

[-32 - 84i - 49] / [-33]

Simplifying further:

[-81 - 84i] / [-33]

Dividing each term by -33:

[-81 / -33 + 84i / -33]

Simplifying:

81 / 33 - 84i / 33

Therefore, z1 / z2 = 2.4545 - 2.5455i

I hope this helps you! Let me know if you have any further questions.