Question

Z1=2+5i z2=-3-4i найти z1/z2​

Answer 1

Ответ: решение смотри на фотографии

Объяснение:

Answer 2

To find the division of complex numbers, we need to multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a complex number a + bi is given by a - bi, where "a" and "b" are real numbers.

Given: z1 = 2 + 5i z2 = -3 - 4i

Conjugate of z2: -3 + 4i

Now, let's perform the division:

z1/z2 = (z1 * conjugate(z2))/(z2 * conjugate(z2))

Substituting the values:

z1/z2 = (2 + 5i) * (-3 + 4i)/((-3 - 4i) * (-3 + 4i))

Expanding the numerator and denominator:

z1/z2 = (-6 - 8i + 15i - 20)/(-9 + 12i - 12i - 16i^2)

Since i^2 = -1:

z1/z2 = (-6 + 7i - 20)/(-9 - 16(-1))

Simplifying:

z1/z2 = (-26 + 7i)/(-9 + 16)

z1/z2 = (-26 + 7i)/7

Dividing each term by 7:

z1/z2 = -26/7 + (7i)/7

z1/z2 = -26/7 + i

Therefore, z1/z2 = -26/7 + i.