1. Simplify the dot product $(-6,3) \cdot (4,-2)$. The dot product formula is $a \cdot b = a_1b_1 + a_2b_2$. Calculate: $(-6)(4) + (3)(-2) = -24 - 6 = -30$. 2. Evaluate $(-i)^{16} \cdot (-i)^6$. Recall $i^2 = -1$, so $-i = -1 \cdot i$. Calculate powers: $(-i)^{16} = ((-i)^2)^8 = (-1)^8 = 1$. $(-i)^6 = ((-i)^2)^3 = (-1)^3 = -1$. Multiply: $1 \times (-1) = -1$. Answer: (b) -1. 3. For any complex number $z$, $|z|$ is equal to? By definition, $|z|$ is the modulus of $z$. Answer: (a) $|z|$. 4. If $z = 3i - 4$, then $z + \overline{z} = ?$ Conjugate $\overline{z} = -4 - 3i$. Sum: $(3i - 4) + (-4 - 3i) = -8 + 0i = -8$. Answer: (c) -8. 5. If $z$ is any real number $x$, then its conjugate is? For real $x$, conjugate is $x$ itself. Answer: (a) $x$. 6. Calculate $(1 + i)^3$. Use binomial expansion: $(1 + i)^3 = 1 + 3i + 3i^2 + i^3$. Recall $i^2 = -1$, $i^3 = i^2 \cdot i = -i$. Simplify: $1 + 3i - 3 - i = (1 - 3) + (3i - i) = -2 + 2i$. Answer: (a) $-2 + 2i$. 7. Real part of $2i (3 - 5i)$. Multiply: $2i \times 3 = 6i$, $2i \times (-5i) = -10i^2 = -10(-1) = 10$. Sum: $10 + 6i$. Real part: 10, Imaginary part: 6. Answer: (b) (10, 6). 8. Value of $i^{-7}$. Rewrite: $i^{-7} = \frac{1}{i^7}$. Since $i^4 = 1$, $i^7 = i^{4+3} = i^4 \cdot i^3 = 1 \cdot (-i) = -i$. So $i^{-7} = \frac{1}{-i} = -\frac{1}{i} = -(-i) = i$. Answer: (b) $i$. 9. If $z_1 = 2 + 3i$, $z_2 = 1 - i$, find $|z_1 z_2|$. Calculate $|z_1| = \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13}$. Calculate $|z_2| = \sqrt{1^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2}$. Product modulus: $|z_1 z_2| = |z_1| \times |z_2| = \sqrt{13} \times \sqrt{2} = \sqrt{26}$. Answer: (b) $\sqrt{26}$. 10. If $n$ is even integer, then $(i)^n$ is? Since $i^4 = 1$, powers of $i$ cycle every 4. For even $n$, $i^n$ is either $1$ or $-1$. Answer: (c) 1 or -1. 11. If $a > 0$ and $b < 0$, then $ab$ is? Positive times negative is negative. Answer: (b) $ab < 0$. 12. Any matrix of order $m \times 1$ is called? A matrix with one column is a column matrix. Answer: (b) column Matrix.