If P and Q are two compex numbers, then the modulus of the quotient of P ans Q is :

Options

A. Greater than the quotient of their moduli
B. Less than the quotient of their moduli
C. Less than or equal to the quotient of their moduli
D. Equal to the quotient of their moduli

Answer

D

Explanation

The two complex numbers are
`P=x+iy andQ=alpha+ibeta`
Quotient `=P/Q=(x+iy)/(alpha+ibeta),|(P)/(Q)|=|(x+iy)/(alpha+ibeta)|`
`=(sqrt(x^(2)+y^(2)))/(sqrt(alpha^(2)+beta^(2)))=sqrt((x^(2)+y^(2))/(alpha^(2)+beta^(2)))=|(Z_(1))/Z_(2)|=|(Z_(1))/(Z_(2))|`
Hence, the quotient of their modulus is equal to the quotient of their moduli.