Modulus of Complex Numbers

Let w=-√3/2 + 1/2 i calculate the modulus and argument.

• 3, 120^o

• 5, 270^o

• 1, 150^o

• Not Possible

Calculate the modulus (R) and argument (θ) for z = 4 + 9i. Give the argument between -π < θ < π.

• R = 9.05, θ = 1.99 rad or 114°

• R = 9.8, θ = 1.2 rad or 66°

• R = 97, θ = 1.2 rad or 66°

• R = 9.8, θ = 5.13 rad or 294°

Answer explanation

Calculate the modulus (R) and argument (θ) for z = -5 + 3i Give the argument between -π < θ < π.

• R = 5.83, θ = 0.54 rad or 31°

• R = 34, θ = 2.6 rad or 149°

• R = 5.83, θ = 3.7 rad or 211°

• R = 5.83, θ = 2.6 rad or 149°

Answer explanation

Calculate the modulus (R) and argument (θ) for z = -7 - 5i
Give the argument between -π < θ < π.

• R = 8.6, θ = -2.5 rad or -144.5°

• R = 8.6, θ = 3.8 rad or 215.5°

• R = 74, θ = 0.6 rad or 35.5°

• R = 8.6 , θ = 4.1 rad or 234.5 °

Answer explanation

Calculate the modulus (R) and argument (θ) for z = 3 - 7i Give the argument between -π < θ < π.

• R = √58, θ = -1.2 rad or -66.8°

• R = 7.6, θ = 1.2 rad or 66°

• R = √58, θ = 5.1 rad or 293.2°

• R = 7.6 , θ = 1.98 rad or 113.2 °

Answer explanation

The modulus of 5 + 4i is

• 41

• -41

• √41

• -√41

• 2

• 1

• 5

• 8

If a + ib = c + id, then

• A² + c² =0

• B² + c²=0

• B²+D²=0

• A²+B²=C²+D²

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

• 3

• 4

• 5

• √7

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)