SOLUTION: Hi, Can you help me with this exercise,please It says the following z1=-5+4i z2=K+6i Find k such that: (z1+z2)/z1+i I found the complex conjugate of z1+i which i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hi, Can you help me with this exercise,please It says the following z1=-5+4i z2=K+6i Find k such that: (z1+z2)/z1+i I found the complex conjugate of z1+i which i      Log On


   

Question 942146: Hi,
Can you help me with this exercise,please
It says the following
z1=-5+4i
z2=K+6i
Find k such that:
(z1+z2)/z1+i
I found the complex conjugate of z1+i which is :-5-5i and then I multiplied top and bottom with this conjugate and I've got a really big fraction which I don't know what to do with it.Can you plese help me with this
Thank you so much

Found 2 solutions by richard1234, rothauserc:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
http://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.941938.html

Still, you did not ask a complete question. (z1+z2)/z1+i is simply a number, not a statement or equality. As a math tutor and someone who has written mock test problems, what I just read does not make sense as a math question.

Example questions are:
Find k such that (z1+z2)/(z1+i) = 1
Find k such that |(z1+z2)/(z1+i)| > 1
Find k such that (z1+z2)/(z1+i) ...

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
note that i^2 = -1
first determine the conjugate
z1 + i = -5 +4i +i = -5 +5i
conjugate is (-5 -5i)
z1 + z2 = -5+4i + K+6i = k +10i -5
multiply numerator and denominator by the conjugate
note that we assume k is real
((k+10i-5)*(-5-5i)) / ((-5+5i)*(-5-5i))
note that ((-5+5i)*(-5-5i)) = 25-25i^2 = 50
(-5ki-5k-25i+75) / 50
divide numerator and denominator by 5
-ki-k-5i+15 /10
i(-k-5)-k+15 / 10
i(-k/10 -1/2)-(k/10)+(3/2)