The equation of the line joining the complex numbers -5 + 4i and 7 + 2i can be expressed in the form az + b \overline{z} = 38 for some complex numbers a and b. Find the ordered pair (a, b).

Guest May 4, 2019

edited by
Guest
May 4, 2019

edited by Guest May 4, 2019

edited by Guest May 4, 2019

#1**+3 **

\(\text{Both points are on the line so plug them in}\\ a(-5+4i) + b(-5-4i)=38\\ a(7+2i)+b(7-2i) = 38\\ (-5a-5b)+i(4a-4b)=38\\ (7a+7b)+i(2a-2b)=38\)

\(-5(a+b)-14(a+b)=-38\\ -19(a+b)=-38\\ a+b=2\)

\(-5(2) + i(4a-4(2-a))=38\\ i(8a-8)=48\\ i(a-1)=6\\ a-1 = -6i\\ a=1-6i\\ b=2-(1-6i) = 1+6i\)

\((a,b) = (1-6i,1+6i)\)

.Rom May 4, 2019

#2**0 **

Hi Rom,

Thanks for your answer

but...

I do not understand that initial plug in. Why have you used the conjugates??

Could you explain a little more please.

Melody May 5, 2019