Which of the following are correct for any tw | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For any two complex numbers $z_1$ and $z_2$:$1$. The modulus of the product is the product of the moduli: $|z_1 z_2| = |z_1| |z_2|$. Thus,$(a)$ is

Vedclass · Accepted Answer

Both $(a)$ and $(c)$

Vedclass · Answer

(D) For any two complex numbers $z_1$ and $z_2$:$1$. The modulus of the product is the product of the moduli: $|z_1 z_2| = |z_1| |z_2|$. Thus,$(a)$ is correct.$2$. The argument of the product is the sum of the arguments: $arg(z_1 z_2) = arg(z_1) + arg(z_2)$. Thus,$(b)$ is incorrect.$3$. The triangle inequality for moduli states that $|z_1 - z_2| \geqslant ||z_1| - |z_2||$. Thus,$(c)$ is correct.Therefore,both $(a)$ and $(c)$ are correct.

Which of the following are correct for any two complex numbers $z_1$ and $z_2$?

Similar Questions

If $x+iy = (1+i)^6 - (1-i)^6$,then which one of the following is true?

If $z=x+iy$ is a complex number such that $\bar{z}^{\frac{1}{3}}=a+ib$,then the value of $\frac{1}{a^2+b^2}\left(\frac{x}{a}+\frac{y}{b}\right)$ is equal to

Let $z_1$ and $z_2$ be any two non-zero complex numbers such that $3|z_1| = 4|z_2|$. If $z = \frac{3z_1}{2z_2} + \frac{2z_2}{3z_1}$,then:

If $x = 1 + 2i$,then the value of $x^3 + 7x^2 - x + 16$ is

If $z_1$ and $z_2$ are any two complex numbers,then $|z_1 + \sqrt{z_1^2 - z_2^2}| + |z_1 - \sqrt{z_1^2 - z_2^2}|$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module