Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 14

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IMPORTANT

Earn 100

The solution of the equation $|z| - z = 1 + 2 i$ is

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Important Questions on Complex Numbers

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NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 15

If

2 x = 3 + 5 i

, then what is the value of

2 x^{3} + 2 x^{2} - 7 x + 72

?

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IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 16

In the argand diagram, if $O, P$ and $Q$ represent respectively, the origin, the complex numbers $(z)$ and $(z + i z)$ , then the $∠ O P Q$ is

$I .$ $\frac{2 π}{3}$
$II .$ $\frac{π}{2}$
$III .$ $\frac{π}{3}$

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IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 17

What is one of the square roots of

3 + 4 i

, where

i = \sqrt{- 1}

?

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Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 18

If the number

\frac{z - 1}{z + 1}

is purely imaginary, then

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Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 19

If

|z_{1}| = |z_{2}| = \dots . = |z_{n}| = 1,

then

|\frac{1}{z_{1}} + \frac{1}{z_{2}} + \dots \dots + \frac{1}{z_{n}}|

.

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Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 20

If

|z_{1}| = |z_{2}|

and

\arg (\frac{z_{1}}{z_{2}}) = π

, then

z_{1} + z_{2}

is equal to

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Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 21

a, b, c

are three complex number on the unit circle

|z| = 1

, such that

a b c = a + b + c

. Then

| a b + b c + c a |

is equal to

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Mathematics Crash Course NDA & NA EE>Chapter 15 - Complex Numbers>Exercise 1>Q 22

Let arg

(z_{k}) = \frac{(2 k + 1) π}{n}

where

k = 1, 2, 3, 4 . . ., n

. If arg

(z_{1} z_{2} z_{3} . . . z_{n}) = π

, then

n

must be of form

(m \in I)