When the polarizer axis sits at 90 degrees to the field, the projection is zero and no light gets through, which is the crossed-polarizer result. The clean zero relies on an exact 90-degree alignment and an ideal polarizer with no leakage. Real crossed polarizers pass a small extinction ratio, because alignments, diattenuation, and stray fields are measured quantities with finite precision.
A crossed polarizer sends the axis component to zero before any intensity claim. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A crossed polarizer has zero pass component
With crossed orientation, the parallel slot is exactly 0