Question:
A complex number is given by \(z = \dfrac{1+2i}{1-(1-i)^2}\). What is the modulus of z?
एक सम्मिश्र संख्या \(z = \dfrac{1+2i}{1-(1-i)^2}\) द्वारा दी गई है। z का मापांक (modulus) क्या है?
Options:
- 1
- 4
- 2
- \(\dfrac{1}{2}\)
- 1
- 4
- 2
- \(\dfrac{1}{2}\)
Correct Answer: a)
Explanation:
\((1-i)^2 = 1 – 2i + i^2 = -2i\).
\(z = \dfrac{1+2i}{1 – (-2i)} = \dfrac{1+2i}{1+2i} = 1\).
Modulus \(|z| = |1| = 1\).
\((1-i)^2 = 1 – 2i + i^2 = -2i\)।
\(z = \dfrac{1+2i}{1 – (-2i)} = \dfrac{1+2i}{1+2i} = 1\)।
अतः मापांक \(|z| = |1| = 1\)।