Home / NDA / Questions / Complex Numbers and Quadratic Equations / Question NDA 2017 Maths · Mathematics · Complex Numbers and Quadratic Equations · easy
If z=(3+4i)/(1-2i), then |z| equals Single correct option
If
z = 3 + 4 i 1 − 2 i z=\dfrac{3+4i}{1-2i} z = 1 − 2 i 3 + 4 i , then
∣ z ∣ |z| ∣ z ∣ equals
A. 5 5 5 B. 5 5 + 1 \dfrac{5}{\sqrt5}+1 5 5 + 1 C. 5 / 5 \sqrt{5}/5 5 /5 D. 5 \sqrt5 5 Show answer and solution Answer: (D) 5 \sqrt5 5
∣ z ∣ = ∣ 3 + 4 i ∣ ∣ 1 − 2 i ∣ = 5 5 = 5 |z|=\dfrac{|3+4i|}{|1-2i|}=\dfrac{5}{\sqrt5}=\sqrt5 ∣ z ∣ = ∣1 − 2 i ∣ ∣3 + 4 i ∣ = 5 5 = 5 . There is no need to rationalise; the modulus of a quotient is the quotient of the moduli. Option 5 forgets to divide by
∣ 1 − 2 i ∣ |1-2i| ∣1 − 2 i ∣ .
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