NDA || Mathematics || Algebra || Complex Numbers || Quiz 2020

Z= (1-i)/(1+i) can also be expressed as

What is the argument of (2-3i)/(-5+i)

Let α and β be real numbers and z be a complex number. If z² + αz + β = 0 has two distinct non-real roots with Re(z) = 1, then it is necessary that

What is the principal argument of (-1 –i), where

Evaluate (i⁵⁷ + i⁷⁰ + i⁹¹ + i¹⁰¹ + i¹⁰⁴).

The common roots of the equations
z³ + 2z² + 2z + 1 = 0 and z²⁰¹⁷ + z²⁰¹⁸ + 1 = 0 are

What is the value of (1+w-w²)(w), where w is the cube root of unity

Given z₁=2+2√3i and z₂ = 1+i . find the argument of Arg (z₁/z₂)

What is i¹⁰⁰⁰ + i¹⁰⁰¹ + i¹⁰⁰² + i¹⁰⁰³ equal to (where i = √-1)?

The number of non-zero integral solutions of the equation |1 – 2i|^x = 5^x is