Question

Z1=2+7i z2=-11+6iz1+z2=?z1-z2=?z1*z2=?z1/z2=?заранее спасибо

Answer 1

2+7i+(-11+6i)=-9+13i;
2+7i-(-11+6i)=13-i;
(2+7i)*(-11+6i)=-22+12i-77i-42=-64-65i;
(2+7i)/(-11+6i)=(2+7i)*(-11-6i)/(11^2+6^2)=(-22-12i-77i+42)/157=(20-89i)/157;
как-то так

Answer 2

To answer your questions, let's first define the given complex numbers:

- z1 = 2 + 7i - z2 = -11 + 6i

Now, let's calculate the results step by step:

Addition (z1 + z2):

To add two complex numbers, we simply add their real parts and their imaginary parts separately. Applying this to z1 and z2, we get:

z1 + z2 = (2 + 7i) + (-11 + 6i) = (2 - 11) + (7 + 6)i = -9 + 13i

So, z1 + z2 = -9 + 13i.

Subtraction (z1 - z2):

To subtract two complex numbers, we subtract their real parts and their imaginary parts separately. Applying this to z1 and z2, we get:

z1 - z2 = (2 + 7i) - (-11 + 6i) = (2 + 11) + (7 - 6)i = 13 + i

So, z1 - z2 = 13 + i.

Multiplication (z1 * z2):

To multiply two complex numbers, we use the distributive property and the fact that i^2 = -1. Applying this to z1 and z2, we get:

z1 * z2 = (2 + 7i) * (-11 + 6i) = 2*(-11) + 2*6i + 7i*(-11) + 7i*6i = -22 + 12i - 77i + 42i^2 = -22 + 12i - 77i + 42*(-1) = -22 + 12i - 77i - 42 = -64 - 65i

So, z1 * z2 = -64 - 65i.

Division (z1 / z2):

To divide two complex numbers, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of a complex number a + bi is a - bi. Applying this to z1 and z2, we get:

z1 / z2 = (2 + 7i) / (-11 + 6i) * (-11 - 6i) / (-11 - 6i) = (-22 - 12i - 77i - 42) / (121 + 66i - 66i - 36i^2) = (-64 - 89i) / (121 + 36) = (-64 - 89i) / 157

So, z1 / z2 = (-64 - 89i) / 157.

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