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Operations with Radicals and Complex Numbers Quiz

#1

What is the square root of 49?

7
Explanation

Square root of a number is a value that, when multiplied by itself, gives the original number.

#2

Which of the following is an irrational number?

π
Explanation

Pi (π) is an irrational number as it cannot be expressed as a simple fraction.

#3

What is the absolute value of -8?

8
Explanation

Absolute value is the distance of a number from zero on the number line, ignoring its sign.

#4

What is the real part of the complex number 5 + 2i?

5
Explanation

The real part of a complex number a + bi is 'a.'

#5

What is the square root of -1?

i
Explanation

The square root of -1 is the imaginary unit 'i.'

#6

What is the modulus of the complex number -3 + 4i?

5
Explanation

The modulus of a complex number a + bi is the square root of the sum of the squares of its real and imaginary parts.

#7

What is the conjugate of 4 + 3i?

4 - 3i
Explanation

The conjugate of a complex number a + bi is a - bi.

#8

What is the product of (2 + 3i) and (4 - 5i)?

8 - 7i
Explanation

Multiplying complex numbers involves distributing and combining like terms.

#9

What is the simplified form of √75?

15√3
Explanation

Breaking down the square root into prime factors yields the simplified form.

#10

What is the cube root of -64?

-4
Explanation

The cube root of a number is the value that, when cubed, gives the original number.

#11

What is the product of (3 + 2i) and its conjugate?

9
Explanation

Multiplying a complex number by its conjugate eliminates the imaginary part.

#12

What is the simplified form of √(-16)?

4i
Explanation

The square root of a negative number is represented using the imaginary unit 'i.'

#13

What is the value of √(-9)?

3i
Explanation

The square root of a negative number is represented using the imaginary unit 'i.'

#14

What is the principal argument of the complex number 2 - 2√3i?

5π/6
Explanation

The principal argument is the angle formed between the complex number and the positive x-axis.

#15

What is the argument of the complex number -2 + 2i?

-π/4
Explanation

The argument is the angle formed between the complex number and the positive x-axis.

#16

What is the cube root of -8?

-2
Explanation

The cube root of a negative number is the value that, when cubed, gives the original negative number.

#17

What is the argument of the complex number 1 + i?

π/4
Explanation

The argument is the angle formed between the complex number and the positive x-axis.

#18

What is the principal argument of the complex number -4 + 4√3i?

π/3
Explanation

The principal argument is the angle formed between the complex number and the positive x-axis.

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