Complex Numbers and Quadratic Equations MATHS - Complex Numbers and Quadratic Equations

The real value of $\alpha$ for which the expression $\frac{1-\text{i}\sin\alpha}{1+2\text{i}\sin\alpha}$ is purely real is:

1. $(\text{n}+1)\frac{\pi}{2}$

2. $(2\text{n}+1)\frac{\pi}{2}$

3. $\text{n}\pi$

4. None of these, where $\text{n}\in\text{N}$

The value of $(\text{z}+3)(\bar{\text{z}}+3)$ is equivalent to:

1. |z + 3|²
2. |z - 3|
3. z² + 3
4. None of these.

$\sin\text{x}+\text{i}\cos2\text{x}$ and $\cos\text{x}-\text{i}\sin2\text{x}$ are conjugate to each other for:

1. $\text{x}=\text{n}\pi$

2. $\text{x}=\Big(\text{n}+\frac{1}{2}\Big)\frac{\pi}{2}$

3. $\text{x}=0$

4. no value of x

The complex number z which satisfies the condition $\Big|\frac{\text{i}+\text{z}}{\text{i}-\text{z}}\Big|=1$ lies on:

1. Circle x² + y² = 1
2. The x-axis
3. The y-axis
4. The line x + y = 1