NDA 2022 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

√(-2)·√(-3)=√6. 2. zbar z=|z|^2 for every complex number z.

Single correct option

Consider the following statements:
1.

\sqrt{-2}\cdot\sqrt{-3}=\sqrt6

.
2.

z\bar z=|z|^2

for every complex number

z

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (B) 2 only

Statement 1 is false:

\sqrt{-2}\sqrt{-3}=(i\sqrt2)(i\sqrt3)=-\sqrt6

, because the product rule for radicals needs non-negative numbers. Statement 2 is true:

(x+iy)(x-iy)=x^2+y^2

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