=2+2bi+i-b (note: i*i=- 1)

Separate the real part from the imaginary part, and you get it.

=(2-b)+(2b+ 1)i

(Because the complex number (1+bi)(2+i) is purely imaginary, the real part is equal to 0 and the imaginary part is not equal to 0), so 2-b=0, 2b+ 1 is not equal to 0.

The solution is b=2.

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