# Complex Numbers · Mathematics · NDA

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NDA Mathematics 21 April 2024
If $z$ is any complex number and $iz^2 + z - z + i = 0$, where $i = \sqrt{-1}$, then what is the value of $(|z| + 1)^2$?
NDA Mathematics 21 April 2024
If $x, y$ and $z$ are the cube roots of unity, then what is the value of $xy + yz + zx$?
NDA Mathematics 21 April 2024
Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1 + z_2}{z_1 - z_2}\right| = 1$, then what is $\operatorname{Re} \left(\frac{z_1}{... NDA Mathematics 21 April 2024 If$\omega \neq 1$is a cube root of unity, then what are the solutions of$(z-100)^3 + 1000 = 0$? NDA Mathematics 21 April 2024 What is$(1 + i)^4 + (1 - i)^4$equal to, where$i=\sqrt{-1}$? NDA Mathematics 3 September 2023 If z z̅ = |z + z̅ |, where z = x + iy, i =$\sqrt{-1}$, then the locus of z is a pair of: NDA Mathematics 3 September 2023 What is the value of$\sqrt{12+5 i}+\sqrt{12-5 i}$where$i=\sqrt{-1}$? NDA Mathematics 3 September 2023 Which one of the following is a square root of$-\sqrt{-1} $? NDA Mathematics 3 September 2023 What are the roots of equation-I ? NDA Mathematics 3 September 2023 Which one of the following is a root of equation-II? NDA Mathematics 3 September 2023 What is the number of common roots of equation-I and equation-II? NDA Mathematics 16 April 2023 If ω is a non-real cube root of 1, then what is the value of$\left|\frac{1-\omega}{\omega+\omega^2}\right| ?$... NDA Mathematics 16 April 2023 If α and β are the distinct roots of equation x2 - x + 1 = 0, then what is the value of$\left|\frac{\alpha^{100}+\beta^{100}...
NDA Mathematics 16 April 2023
If 2 - i√3 where i = √-1 is a root of the equation x2 + ax + b = 0, then what is the value of (a + b)? ...
NDA Mathematics 16 April 2023
If $z=\frac{1+i √{3}}{1-i √{3}}$ where i = √-1 then what is the argument of z ?
NDA Mathematics 16 April 2023
If z is a complex number such that $\frac{z-1}{z+1}$ is purely imaginary, then what is |z| equal to ?
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