Find the real number x if (x-2i)(1+i)is purely imaginary.
(x-2i)(1+i) = x+2 + some i stuff
If it's purely imaginary, the real part, x+2 = 0
M nt understanding whether it's purely imaginary or no
To find the real number x if the expression (x-2i)(1+i) is purely imaginary, we need to first expand the expression and then analyze it.
Let's start by expanding the expression:
(x - 2i)(1 + i) = x * 1 + x * i - 2i * 1 - 2i * i
= x + xi - 2i - 2i^2
To simplify further, let's recall that i^2 is equal to -1:
(x + xi - 2i - 2i^2) = x + xi - 2i + 2
= x + xi - 2i + 2
= x + xi - 2i + 2
= (x + 2) + (x - 2)i
Now, we want the expression to be purely imaginary, which means the real part (x + 2) should be zero. This implies that:
x + 2 = 0
To solve for x, we simply isolate the variable:
x = -2
Therefore, the value of x that makes the expression (x-2i)(1+i) purely imaginary is x = -2.