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Digital SAT
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Ratio of Moduli of Complex Numbers

Hard Additional Math Topics Complex Numbers

Consider a complex number $z$ defined as follows:

$$z = 3 + 4i$$

Where $i$ is the imaginary unit. The modulus of a complex number $z = a + bi$ is given by the formula:

$$|z| = ext{sqrt}(a^2 + b^2)$$

Let $w$ be another complex number defined as:

$$w = 1 - 2i$$

Calculate the value of the ratio of the modulus of $z$ to the modulus of $w$ and express your answer as a simplified fraction or decimal.

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