Polar Multiplication

Question

If two complex numbers have moduli 2 and 5 and arguments 40 degrees and 80 degrees respectively, then the modulus and argument of their product are correctly given by which pair?

RankGuru · Accepted Answer

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.

Polar Multiplication

Select the correct option:

🔒 Solution Hidden from View

More complex numbers and quadratic equations Practice Questions

The set of all complex numbers z satisfying the equation given by the ratio condition arg of the qua...

If the equation x^2 - (k - 3)x + k = 0 has both roots real, then the set of all real values of the p...

For any complex number z, the expression z multiplied by its conjugate z-bar is always equal to whic...

If alpha and beta are roots of x^2 - 2x + 4 = 0, then the value of the symmetric expression alpha cu...

The values of the real parameter m for which the quadratic equation (m + 1)x^2 + 2(m + 3)x + (m + 8)...

Among all complex numbers z lying on the circle defined by |z| = 1, the maximum value attained by th...

If the two quadratic equations x^2 + bx + c = 0 and x^2 + cx + b = 0, with b not equal to c, share e...

For a complex number z satisfying the constraint |z - 4| ≤ 3, the maximum possible value of the modu...

If one root of the real-coefficient quadratic x^2 + px + q = 0 is the complex number 2 + 3i, then th...

The sum of all the distinct fifth roots of unity in the complex plane, taken together as complex num...

For all real x, the quadratic expression f(x) = x^2 - 6x + 11 attains a minimum value, and that mini...

If alpha and beta are the roots of x^2 - 4x + 1 = 0, then the quadratic equation whose roots are the...

About This Question

Solution