Find the modulus of $z = 3 + 4 i$ .

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What are the eigenvalues of the matrix with rows (6, 2) and (0, 2)?
The curve $y = x^{3} - 12 x + 7$ has two stationary points. Find the difference between their $y$ -coordinates (larger minus smaller).
If $α$ and $β$ are the roots of $x^{2} - 11 x + 30 = 0$ , find $\frac{1}{α} + \frac{1}{β}$ .
If $z = 4 + 2 i$ and $w = 1 - 4 i$ , find the real part of $z w$ .
Find $a \cdot b$ for $a = 0 i - 3 j + 1 k$ and $b = 3 i - 1 j + 1 k$ .
Two independent events have probabilities 0.5 and 0.4. What is the probability that at least one occurs?