Question

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

Answer 1

Answer: -2

Step-by-step explanation:

$\text{(x - 2i)(1 + i)} \\ \\ \implies \text{x + xi - 2i - 2i}^2 \\ \\ \implies \text{(x + 2) + (x - 2)i }\\ \\ \text{For this to be purely imaginary real part must be zero} . \\ \\ \implies \text{x + 2 = 0}\\ \\ \implies \text{x = -2}$

Hope this helps