Exploring Basic Operations with Complex Numbers

What is the primary reason for expanding the real number system to include complex numbers?

• To solve equations that have no real solutions

• To make counting easier

• To simplify arithmetic operations

• To avoid using negative numbers

What does the imaginary unit 'i' represent?

• The square root of 1

• The square root of 0

• The square root of -1

• The square root of 2

What is the value of i squared (i^2)?

• 1

• i

• 0

• -1

How should you treat the imaginary unit 'i' when performing basic operations?

• As a variable

• As a whole number

• As a constant

• As a fraction

What is the result of adding 8 - i and 5 + 4i?

• 3 - 3i

• 13 - 3i

• 3 + 3i

• 13 + 3i

What happens when you add 6i and -6i?

• You get 12i

• You get -12i

• They cancel out to 0

• You get 6

What should you do when you see powers of 'i' like i^6 or i^8?

• Leave them as they are

• Simplify them based on known values of i^2 and i^4

• Convert them to fractions

• Ignore them

What is the simplified form of 4i * -6?

• -24i

• 24i

• -24

• 24

What is the result of 4i^2?

• -4i

• 4i

• -4

• 4

Why do we generally write the real part of a complex number first?

• It's a mathematical convention

• It is required by the associative property

• It avoids confusion

• It makes calculations easier