1. **Problem Statement:** We are given the complex number $z_1 = 2 + i$, where $i^2 = -1$. We need to find: (i) $z_2 = 2 z_1$ and plot it. (ii) The complex conjugate $\overline{z_1}$ and plot it. 2. **Formula and Rules:** - Multiplying a complex number by a real number scales both its real and imaginary parts. - The complex conjugate of $z = a + bi$ is $\overline{z} = a - bi$. 3. **Step (i): Find $z_2 = 2 z_1$** $$z_2 = 2(2 + i) = 2 \times 2 + 2 \times i = 4 + 2i$$ 4. **Step (ii): Find $\overline{z_1}$** $$\overline{z_1} = 2 - i$$ 5. **Explanation:** - Multiplying $z_1$ by 2 doubles both the real part (2 to 4) and the imaginary part (1 to 2). - The conjugate flips the sign of the imaginary part, so $i$ becomes $-i$. 6. **Final answers:** - $z_2 = 4 + 2i$ - $\overline{z_1} = 2 - i$