The value of ${\left(1+i\right)}^3+{\left(1-i\right)}^3$ is equal to

Important Questions on Complex Numbers

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 50

If $z{\left(2-i2\sqrt{3}\right)}^2=i\left(\sqrt{3}+i\right){}^4$, then the amplitude of $z$ is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 51

If $z_1, z_2$ and $z_3$ are complex numbers such that $\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=\left|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}\right|=1$, then $\left|z_1+z_2+z_3\right|$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 52

If ${\left(\sqrt{3}i+1\right)}^{100}=2^{99}\left(a+ib\right),$ then $a^2+b^2$ is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 53

The value of ${\left(1+\sqrt{3}i\right)}^4+{\left(1-\sqrt{3}i\right)}^4$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 54

If the fourth roots of unity are $z_1, z_2, z_3$ and $z_4,$ then $z_1^2+z_2^2+z_3^2+z_4^2$ is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 55

Among the complex number $z$ satisfying condition $\left|z+1-i\right|\le 1,$ the number having the least positive argument is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 57

If the conjugate of $\left(x+iy\right)\left(1-2i\right)$ is $1+i,$ then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Entrances Gallery>Q 60

If $2x=3+5i$, then the value of $2x^3+2x^2-7x+72$ is