Find two complex numbers that have a sum of 10i, a difference of -4 and a product of -29

Question

contestada

Respuesta :

LammettHash LammettHash · Answer 1 · 2019-03-07T19:00:24+01:00

Let these two numbers be [tex]z[/tex] and [tex]w[/tex]. Their sum is [tex]10i[/tex], their difference is -4, and their product is -29:

[tex]z+w=10i[/tex]

[tex]z-w=-4[/tex]

[tex]zw=-29[/tex]

Add the first two equations together to eliminate [tex]w[/tex]:

[tex](z+w)+(z-w)=10i-4\implies 2z=-4+10i\implies z=-2+5i[/tex]

Then

[tex]w=10i-z\implies w=10i-(-2+5i)=2+5i[/tex]

Just to confirm this is correct, check their product:

[tex](-2+5i)(2+5i)=-4+25i^2=-4-25=-29[/tex]

Cetacea Cetacea · Answer 2 · 2022-01-18T11:39:58+01:00

The complex numbers are (-2 + 5i) and (2 + 5i).

Let the complex numbers are (a + ib) and (x + iy).

According to the question:

(a + ib) + (x + iy) = 10i

(a + x) + i(b + y) = 10i

Comparing we get: a + x = 0 or, x = -a,

b + y = 10.

According to the question:

(a + ib) - (x + iy) = -4

(a - x) + i(b - y) = -4

Comparing we get: a - x = -4.

b - y = 0 or, b = y.

Plug x = -a in a - x = - 4

[tex]a-x=-4\\a-(-a)=-4\\2a=-4\\a=-2[/tex]

So, x = -a= 2.

Plug b = y in b + y = 10.

b + y = 10

So, 2b = 10

or, b = 5

So the complex numbers are (-2 + 5i) and (2 + 5i).

Learn more: https://brainly.com/question/12356025