Complex Numbers

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

• √(a^2 + b^2)

• a + b

• a^2 + b^2

• √(a^2 - b^2)

What is the polar form of a complex number z=x+yi?

• r(sinθ−icosθ)

• x + y

• r(cosθ + isiθ) where r=√(x^2 + y^2)

• θ(cosr + isi)

What is the square root of a complex number z?

• w=x+yi such that w^2=z

• √z=x^2−y^2

• w = x + y

• None of the above

In the complex plane, the horizontal axis represents the:

• Imaginary axis

• Real axis

• Polar axis

• Argument axis

The trigonometric form of −1+√3i involves which angle?

• π/3

• 2π/3

• π/4

• π

What does DeMoivre’s Theorem help compute?

• Square roots of real numbers

• Polar angles

• Additive inverses

• Powers and roots of complex numbers

The modulus of a complex number z=3−4i is:

• 3

• 4

• 5

• √7

Which of the following represents a complex number in polar form?

• r(cosθ + isiθ)

• x + yi

• a + b

• √(x^2 + y^2)

The additive inverse of z=3−2i is:

• 3 + 2i

• −3 + 2i

• −3 − 2i

• 2 − 3i

The multiplicative inverse of z=a+bi is:

• a/(a^2 + b^2) - (b/(a^2 + b^2))i

• a + b

• 1/(a + b)

• a^2 - b^2