Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

EASY

11th Maharashtra Board

IMPORTANT

Earn 100

Evaluate: $i^{- 888}$

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Important Questions on Complex Numbers

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Evaluate the following:

i^{30} + i^{40} + i^{50} + i^{60}

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Show that

1 + i^{10} + i^{20} + i^{30}

is a real number.

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Find the values of :

$i^{49} + i^{68} + i^{89} + i^{110}$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Find the values of :

i + i^{2} + i^{3} + i^{4}

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Simplify

: \frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Find the value of

1 + i^{2} + i^{4} + i^{6} + i^{8} + \dots + i^{20} .

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Show that

1 + i^{10} + i^{100} - i^{1000} = 0 .

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 1 - Complex Numbers>EXERCISE

Is

(1 + i^{14} + i^{18} + i^{22})

is a real number? Justify your answer.