#1
What is the square root of 49?
7
ExplanationSquare 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
ExplanationPi (π) is an irrational number as it cannot be expressed as a simple fraction.
#3
What is the absolute value of -8?
8
ExplanationAbsolute 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
ExplanationThe real part of a complex number a + bi is 'a.'
#5
What is the square root of -1?
i
ExplanationThe square root of -1 is the imaginary unit 'i.'
#6
What is the modulus of the complex number -3 + 4i?
5
ExplanationThe 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
ExplanationThe conjugate of a complex number a + bi is a - bi.
#8
What is the product of (2 + 3i) and (4 - 5i)?
8 - 7i
ExplanationMultiplying complex numbers involves distributing and combining like terms.
#9
What is the simplified form of √75?
15√3
ExplanationBreaking down the square root into prime factors yields the simplified form.
#10
What is the cube root of -64?
-4
ExplanationThe 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
ExplanationMultiplying a complex number by its conjugate eliminates the imaginary part.
#12
What is the simplified form of √(-16)?
4i
ExplanationThe square root of a negative number is represented using the imaginary unit 'i.'
#13
What is the value of √(-9)?
3i
ExplanationThe 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
ExplanationThe 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
ExplanationThe argument is the angle formed between the complex number and the positive x-axis.
#16
What is the cube root of -8?
-2
ExplanationThe 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
ExplanationThe 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
ExplanationThe principal argument is the angle formed between the complex number and the positive x-axis.