Exploring Complex Conjugates and Their Applications

What does the function 'real part of z' return when applied to a complex number z = a + bi?

• bi

• b

• a + bi

• a

In formal terms, what does the 'imaginary part of z' function return?

• b

• a + bi

• a

• bi

How is the conjugate of a complex number z = a + bi denoted?

• z+

• z*

• z'

• z-

What is the conjugate of the complex number z = a + bi?

• a + bi

• a - bi

• -a - bi

• -a + bi

When adding a complex number and its conjugate, what is the result?

• a - b

• a + b

• 2b

• 2a

What is the result of adding z = a + bi and its conjugate algebraically?

• a + b

• 2b

• 2a

• a - b

Why is multiplying the numerator and denominator by the conjugate useful in simplifying complex fractions?

• It eliminates the imaginary part

• It results in a real number

• It makes the fraction smaller

• It changes the sign of the imaginary part

What is the simplified form of (1 + 2i) / (4 - 5i) after multiplying by the conjugate of the denominator?

• -6/41 + 13/41 i

• -6/41 - 13/41 i

• 6/41 + 13/41 i

• 6/41 - 13/41 i

What is the result of multiplying a complex number by its conjugate?

• Zero

• A real number

• An imaginary number

• A complex number

What is the magnitude of a complex number squared equivalent to?

• a^2 - 2ab + b^2

• a^2 + 2ab + b^2

• a^2 - b^2

• a^2 + b^2