Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 55

EASY

JEE Advanced

IMPORTANT

Earn 100

If $\arg (z) < 0,$ then $\arg (- z) - \arg (z)$ is equal to

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Important Questions on Complex Numbers

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 56

If

z

is a point on the Argand plane such that

|z - 1| = 1

, then

\frac{z - 2}{z}

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 57

If

C^{2} + S^{2} = 1,

then

\frac{1 + C + i S}{1 + C - i S}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 58

The imaginary part of

(z - 1)

(\cos α - i \sin α) + {(z - 1)}^{- 1} \times (\cos α + i \sin α)

is zero if

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 59

The value of

\frac{{(\sin \frac{π}{8} + i \cos \frac{π}{8})}^{8}}{{(\sin \frac{π}{8} - i \cos \frac{π}{8})}^{8}}

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 60

If

a = \cos \frac{4 π}{3} + i \sin \frac{4 π}{3}

, then the value of

{(\frac{1 + a}{2})}^{3 n}

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 61

The value of

{(\frac{1 + i}{\sqrt{2}})}^{8} + {(\frac{1 - i}{\sqrt{2}})}^{8}

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 62

The value of

\sum_{k = 1}^{10} (\sin \frac{2 π k}{11} - i \cos \frac{2 π k}{11})

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 4 - Complex Numbers>Target Exercises>Q 63

The value of

\frac{4 (\cos 75^{°} + i \sin 75^{°})}{0.4 (\cos 30^{°} + i \sin 30^{°})}

is