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What is the modulus of (3+4i)/(1-2i)? Single correct option
What is the modulus of
3 + 4 i 1 − 2 i \dfrac{3+4i}{1-2i} 1 − 2 i 3 + 4 i ?
A. 5 \sqrt5 5 B. 5 C. 5 3 \dfrac{5}{\sqrt3} 3 5 D. 1 Show answer and solution Answer: (A) 5 \sqrt5 5
Using
∣ z 1 / z 2 ∣ = ∣ z 1 ∣ / ∣ z 2 ∣ |z_1/z_2|=|z_1|/|z_2| ∣ z 1 / z 2 ∣ = ∣ z 1 ∣/∣ z 2 ∣ :
∣ 3 + 4 i ∣ = 5 |3+4i|=5 ∣3 + 4 i ∣ = 5 and
∣ 1 − 2 i ∣ = 5 |1-2i|=\sqrt5 ∣1 − 2 i ∣ = 5 , so the modulus is
5 / 5 = 5 5/\sqrt5=\sqrt5 5/ 5 = 5 . Students sometimes forget to divide by
∣ z 2 ∣ |z_2| ∣ z 2 ∣ or use
1 + 4 1+4 1 + 4 inside the root incorrectly.
Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake