Question

Найти z1+z2. Z1-z2 z1 •z2 z1/z2 Z1=5j Z2= √2-√3j

Answer 1

Ответ: z1+z2=корень из 2+j*(5-корень из 3)

Z1-z2=-корень из 2+j*(корень из 3-5)

Z1*z2=5*( корень из 2-корень из 3*j^2)=5*корень из 3-5*корень из 2*j.

Z1/Z2=5*j*(корень из 2+корень из 3*j)/5=j*корень из 2-корень из 3.

Пошаговое объяснение:

Answer 2

To find z1 + z2, we simply add their real and imaginary components separately:

z1 = 5j

z2 = √2 - √3j

z1 + z2 = (0 + √2) + (5 - √3)j

Therefore, z1 + z2 = √2 + 5j - √3j.

To find z1 - z2, we simply subtract their real and imaginary components separately:

z1 = 5j

z2 = √2 - √3j

z1 - z2 = (0 - √2) + (5 + √3)j

Therefore, z1 - z2 = -√2 + 5j + √3j.

To find z1•z2, we multiply their real and imaginary components separately:

z1 = 5j

z2 = √2 - √3j

z1•z2 = (0 - 5√3) + (5√2)j

Therefore, z1•z2 = -5√3 + 5√2j.

To find z1/z2, we first need to multiply the numerator and denominator by the complex conjugate of z2, which is √2 + √3j:

z1 = 5j

z2 = √2 - √3j

z2* = √2 + √3j

z1/z2 = (5j / (√2 - √3j)) * (√2 + √3j / √2 + √3j)

Simplifying the denominator:

z1/z2 = (5j(√2 + √3j)) / (2 + 3)

z1/z2 = 5j(√2 + √3j) / 5

z1/z2 = √2 + √3j

Therefore, z1/z2 = √2 + √3j.

Note: j is the imaginary unit, defined as j² = -1.