If real parts of -5-12 i , 5+12 i are positive values, the real part of -8-6 i is a negative value and a+i b= -5-12 i + 5+12 i -8-6 i then 2 a+b=

Step-by-step solution

Let -5-12 i =a+b i, a 0 -5-12 i=(a+b i)^2 So a^2-b^2=-5 and 2 a b=-12 Now, a^2+b^2= (a^2-b^2 )^2+4 a^2 b^2 = (-5)^2+(-12)^2 = 169 =13 aligned & a^2-b^2=-5, a^2+b^2=13 2 a^2=8 a=2 ( a 0) & and b= -12 4 =-3 . So, -5-12 i =2-3 i aligned Similarly, we get 5+12 i =3+2 i and -8-6 i =-1+3 i Now, a+b i= -5-12 i + 5+12 i -8-6 i aligned & Now, a+b i= -5-12 i + 5+12 i -8-6 i & = 2-3 i+3+2 i -1+3 i = 5-i -1+3 i -1-3 i -1-3 i aligned = -8-14 i 10 = -4 5 - 7 5 i a= -4 5 and b= -7 5 So, 2 a+b= -8 5 - 7 5 = -15 5 =-3