Polar Multiplication

Multiplying two complex numbers in polar form multiplies their moduli and adds their arguments, a defining property exploited throughout JEE Advanced. With moduli 2 and 5, the product modulus is 2·5 = 10. With arguments 40 degrees and 80 degrees, the product argument is 40 + 80 = 120 degrees, which already lies in the principal range. Hence the product has modulus 10 and argument 120 degrees. Option modulus 7 wrongly adds the moduli instead of multiplying. Option argument 40 degrees forgets to add the second angle. Option modulus 3 and argument 3200 degrees confuses subtraction and multiplication of the angles. Hence the product is modulus 10 at 120 degrees. Plausibility check: the modulus of a product always equals the product of moduli, so 10 is forced, and adding arguments rotates the result, giving 120 degrees, both consistent with the geometric scaling-and-rotation interpretation of complex multiplication.