Given : √5+12i+√5−12i√5+12i−√5−12i=a+ib
√5+12i+√5−12i√5+12i−√5−12i=(√5+12i+√5−12i)2(5+12i)−(5−12i)=5+12i+5−12i+2√(5+12i)√(5−12i)24i
We know that,
√a+ib=±[√12(√a2+b2+a)+i√12(√a2+b2−a)]∴√5+12i=±(3+2i)
Similarly,
√5−12i=±(3−2i)∴a+ib=10±2(3+2i)(3−2i)24i⇒a+ib=10±2624i⇒a+ib=−3i2 and a+ib=2i3
But as given in question b<0
Hence a=0, b=−32
So, value of a−2b=3