NDA 2024 Maths · Mathematics · Complex Numbers and Quadratic Equations · easy

The conjugate of (1+i)/(1-i) is -i. 2. If |z1|=|z2| then z1=z2.

Single correct option

Which of the statements is/are correct?
1. The conjugate of

\dfrac{1+i}{1-i}

-i

.
2. If

|z_1|=|z_2|

then

z_1=z_2

Show answer and solution

Answer: (A) 1 only

\frac{1+i}{1-i}=\frac{(1+i)^2}{2}=i

, whose conjugate is

-i

, so 1 is true. Equal moduli only mean the points lie on the same circle about the origin, e.g.

1

and

-1

, so 2 is false.

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