Let z1 and z2 be two non-zero complex numbers. Then

Question

Let z1 and z2 be two non-zero complex numbers. Then (A) Principal value of arg (z1 z2) may not be equal to Principal value of arg z1+ Principal value of L2 (B) Principal value of arg (z1 z2)= Principal value of arg z1+ Principal value of arg z2 (C) Principal value of arg (z1 / z2)= Principal value of arg z1- Principal value of arg z2 (D) Principal value of arg (z1 / z2) may not be arg z1- arg z2

Tardigrade Admin · Accepted Answer

arg (z1 z2)= underset1L t+ underset2L t+2 k π arg (z1 / z2)= arg z1- underset2L t+2 k π

Q. Let $z_{1}$ and $z_{2}$ be two non-zero complex numbers. Then

Principal value of $ar g (z_{1} z_{2})$ may not be equal to Principal value of $ar g z_{1} +$ Principal value of $L_{2}$

Principal value of $ar g (z_{1} z_{2}) =$ Principal value of $ar g z_{1} +$ Principal value of $ar g z_{2}$

Principal value of $ar g (z_{1} / z_{2}) =$ Principal value of $ar g z_{1} -$ Principal value of $ar g z_{2}$

Principal value of $ar g (z_{1} / z_{2})$ may not be $ar g z_{1} - ar g z_{2}$

$ar g (z_{1} z_{2}) = 1 L t + 2 L t + 2 kπ$ $ar g (z_{1} / z_{2}) = ar g z_{1} - 2 L t + 2 kπ$

Q. Let z1​ and z2​ be two non-zero complex numbers. Then

Principal value of arg(z1​z2​) may not be equal to Principal value of argz1​+ Principal value of L2​

Principal value of arg(z1​z2​)= Principal value of argz1​+ Principal value of argz2​

Principal value of arg(z1​/z2​)= Principal value of argz1​− Principal value of argz2​

Principal value of arg(z1​/z2​) may not be argz1​−argz2​