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## Homework Statement

If b is added to c = 3.9i + 3.7j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of c. What is the magnitude of b?

**2. The attempt at a solution**

I've probably just been staring at these problems for too long...

First of all, is it valid to say the magnitude of a is the sum of the magnitudes of b and c, that is a=b+c ?

Because if so, then c=sqrt(3.9^2+3.7^2)=a

and if a=b+c then b=a-c= 0 ... which is wrong ):

so what should I do?