Question

Find the real number x if (x-2i )(1+i ) is purely imaginary

Answer 1

It is given that

→(x-2 i )×(1+i )=Purely Imaginary

→x(1 +i) - 2 i× (1+i)→→use (a+b)×(p+q)=a (p+q)+b×(p+q)

→ x + x i -2 i - 2 i²

As, i²= -1

→ x + xi -2 i -2 × (-1)

→ x + x i - 2 i +2 = Purely Imaginary

→ (x+2) +i (x-2)=Purely Imaginary

So, Real part=0

that is, x +2=0

gives , x= -2

Answer 2

Answer:

Real part 0,than x+2=0,x=-2