Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 1

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IMPORTANT

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If $(1 + i) (1 + 2 i) (1 + 3 i) \dots (1 + n i) = a + i b$ , then $2 \times 5 \times 10 \times \dots \times (1 + n^{2})$ is equal to

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Important Questions on Complex Numbers and Quadratic Equations

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Agniveer Vayu

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 2

If

z = \frac{1}{(1 - i) (2 + 3 i)}

, then

|z| =

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 3

If

z = \frac{1}{(2 + 3 i)^{2}}

, then

|z| =

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 4

If

x + i y = (1 + i) (1 + 2 i) (1 + 3 i)

, then

x^{2} + y^{2} =

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 5

If

z = 1 - \cos θ + i \sin θ

, then

|z| =

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 6

If

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

, then

a^{2} + b^{2} =

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 7

Which of the following is correct for any two complex numbers

z_{1}

and

z_{2}

?

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 8

The complex number

z

which satisfy the equation

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

lies on

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Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 9

If

f (z) = \frac{7 - z}{1 - z^{2}}

, where

z = 1 + 2 i

, then

|f (z)| =