When my basement flooded, I had mold which made me sick. I used liquid Pool Chemicals in a field sprayer to wash everything in the basement. It killed the mold and washed right down. This was safe, didn't need any breathing equipment. I'm sure this can be used on our roofs here in the NW.
Bleach is what is usually used to kill mold but as you had used chlorine to kill mold it appears that product works as well. However, roofs usually have algae growing on them and bleach wont work and chlorine may not either. I would be carefull using chlorine. If you mix it with common household products the result will be a toxic gas.
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