Answer
$b=-1$.
Work Step by Step
By definition the dot product of 2 vector $ai+bj$ and $ci+dj$ is: $(ai+bj)(ci+dj)=ac+bd.$ If this product is 0, then the vectors are orthogonal (perpendicular) and hence the enclosed angle is $90^\circ.$
Hence here $v\cdot w=(i+j)(i+bj)=1\cdot1+1\cdot b=0.$
We get the equation: $1+b=0$, hence $b=-1$.
