Argument and Modulus for Complex Numbers

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

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

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

• 3, 120^o

• 5, 270^o

• 1, 150^o

• Not Possible

Consider the complex number in the graph. Given that the argument must be between -π < θ < π, what can you say about the argument, θ?

• θ is negative and -π < θ < -π/2

• θ is negative and -π/2 < θ < 0

• θ is positive and π/2 < θ < π

• θ is positive and 0 < θ < π/2

Answer explanation

Consider the complex number in the graph. Given that the argument must be between -π < θ < π, what can you say about the argument, θ?

• θ is negative and -π < θ < -π/2

• θ is negative and -π/2 < θ < 0

• θ is positive and π/2 < θ < π

• θ is positive and 0 < θ < π/2

Answer explanation

What is the argument of z=3-6i?

• θ=2

• θ=9.36

• θ=2.33

• θ=-1.107

In the polar equation z = 6 (cos(45^o) + i sin(45^o), the modulus is:

What is the modulus of z=-5+2i

• 7i or 33