The modulus of the complex number (1-2i)/(2+i) is:

April 12, 2026Mathematics

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April 12, 2026

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\frac{1-2i}{2+i}$$

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Question 10: The modulus of the complex number $\frac{1-2i}{2+i}$ is:

Step 1: Simplify the complex number by multiplying the numerator and denominator by the conjugate of the denominator. $z = \frac{1-2i}{2+i}$ $z = \frac{1-2i}{2+i} \times \frac{2-i}{2-i}$ $z = \frac{(1)(2) + (1)(-i) + (-2i)(2) + (-2i)(-i)}{2^2 - i^2}$

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You're on a roll — let's solve these questions. Question 10: The modulus of the complex number (1-2i)/(2+i) is: Step 1: Simplify the complex number by multiplying the numerator and denominator by the conjugate of the denominator.

Asked on April 12, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 12, 2026

You're on a roll — let's solve these questions. Question 10: The modulus of the complex number (1-2i)/(2+i) is: Step 1: Simplify the complex number by multiplying the numerator and denominator by the conjugate of the denominator. z = (1-2i)/(2+i) z = (1-2i)/(2+i) × (2-i)/(2-i) z = ((1)(2) + (1)(-i) + (-2i)(2) + (-2i)(-i))/(2^2 - i^2) z = 2 - i - 4i +