AIEEE 2004 | Complex Numbers Question 200 | Mathematics

If $$z = x - iy$$ and $${z^{{1 \over 3}}} = p + iq$$, then

$${{\left( {{x \over p} + {y \over q}} \right)} \over {\left( {{p^2} + {q^2}} \right)}}$$ is equal to :

- 2

- 1

AIEEE 2003

MCQ (Single Correct Answer)

-1

If $$z$$ and $$\omega $$ are two non-zero complex numbers such that $$\left| {z\omega } \right| = 1$$ and $$Arg(z) - Arg(\omega ) = {\pi \over 2},$$ then $$\,\overline {z\,} \omega $$ is equal to

$$- i$$

- 1

$$i$$

AIEEE 2003

MCQ (Single Correct Answer)

-1

Let $${Z_1}$$ and $${Z_2}$$ be two roots of the equation $${Z^2} + aZ + b = 0$$, Z being complex. Further , assume that the origin, $${Z_1}$$ and $${Z_2}$$ form an equilateral triangle. Then :

$${a^2} = 4b$$

$${a^2} = b$$

$${a^2} = 2b$$

$${a^2} = 3b$$

AIEEE 2003

MCQ (Single Correct Answer)

-1

If $${\left( {{{1 + i} \over {1 - i}}} \right)^x} = 1$$ then :

x = 2n + 1, where n is any positive integer

x = 4n , where n is any positive integer

x = 2n, where n is any positive integer

x = 4n + 1, where n is any positive integer.