Let-z-is-complex-number-satisfying-the-equation-z-2-3-i-z-m-2i-0-where-m-R-Suppose-the-equation-has-a-real-root-then-find-the-non-real-root-

Question Number 49151 by rahul 19 last updated on 03/Dec/18

L e t z i s c o m p l e x n u m b e r s a t i s f y i n g

t h e e q u a t i o n z^{2} - (3 + i) z + m + 2 i = 0,

w h e r e m ϵ R . S u p p o s e t h e e q u a t i o n

h a s a r e a l r o o t, t h e n f i n d t h e n o n r e a l r o o t ?

Answered by mr W last updated on 03/Dec/18

z_{1} = a = t h e r e a l r o o t

z_{2} = p + q i = t h e n o n r e a l r o o t

a + p + q i = 3 + i

a (p + q i) = m + 2 i

q = 1

a + p = 3

a q = 2 \Rightarrow a = 2

a p = m

\Rightarrow p = 1

\Rightarrow z_{2} = 1 + i

m = 2

Commented by rahul 19 last updated on 04/Dec/18

thanks sir ��