If 1 - i z z - i = 1 , then z lies on

a line not passing through origin

MEDIUM

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Which of the following is NOT associated with Renaissance humanism?

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Important Questions on Complex Numbers and Quadratic Equations

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Some meta-directing substituents in aromatic substitution are given. Which one is most deactivating?

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of sum

\sum_{n = 1}^{13} (i^{n} + i^{n + 1}), where i = \sqrt{- 1},

equals

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The compounds $A$ and $B$ in the following reaction are, respectively:

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Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

For all complex numbers

z

of the form

1 + i α, α \in R,

z^{2} = x + i y,

then

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The correct IUPAC name of the following compound is:

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EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The concept of “Omnis cellula-e cellula” regarding cell division was first proposed by:

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Aromatic electrophilic substitution reaction that is reversible is

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

In the following structure, the double bonds are marked as

I, II, III

and

IV

Geometrical isomerism is not possible at the site(s):

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

For positive integers

n_{1}, n_{2}

the value of the expression

{(1 + i)}^{n_{1}} + {(1 + i^{3})}^{n_{1}} + {(1 + i^{5})}^{n_{2}} + {(1 + i^{7})}^{n_{2}}, i = \sqrt{- 1}

is a real number if and only if

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The equation, whose roots are

i, \frac{1 + i}{\sqrt{2}}, \frac{i - 1}{\sqrt{2}},

their conjugates,

- 1 and 1

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

z

is a complex number such that

Re (z) = I m (z)

, then

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

|\frac{1 - i z}{z - i}| = 1,

then

z

lies on

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

(3 + i) z = (3 - i) \bar{z}

, then the complex number

z

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of sum

\sum_{n = 1}^{13} (i^{n} + i^{n + 1})

, where

i = \sqrt{- 1}

, equals

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The complex number which satisfy the equation

z + \sqrt{2} |z + 1| + i = 0

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The value of

\sum_{n = 0}^{100} i^{n!}

equals (where

i = \sqrt{- 1}

)

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

The relation between the real numbers

a

and

b

, which satisfy the equation

\frac{1 - i x}{1 + i x} = a - i b

, for some real value of

x

, is

MEDIUM

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Let

z

be a complex number such that the imaginary part of

z

is nonzero and

a = z^{2} + z + 1

is real. Then

a

cannot take the value

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

If $a = \cos α + i \sin α, b = \cos β + i \sin β$ , $c = \cos γ + i \sin γ$ and $\frac{b}{c} + \frac{c}{a} + \frac{a}{b} = 1$ , then $\cos (β - γ) + \cos (γ - α) + \cos (α - β)$ is equal to $(where i = \sqrt{- 1})$

EASY

Mathematics>Algebra>Complex Numbers and Quadratic Equations>Complex Numbers

Evaluate

{(- \sqrt{- 1})}^{4 n + 3}, n \in N

Which of the following is NOT associated with Renaissance humanism?

Important Questions on Complex Numbers and Quadratic Equations

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