Quiz for Applications of Imaginary Numbers

June 27th, 2008

Here are some questions for extra credit. Answers to these are sprinkled throughout our tutorial. Perfect for the curious student who asks in class about the utility of imaginary numbers. You are more than welcome to cut and paste these and use them however you wish. Two versions provided so you can mix and match to construct unique tests.

1. Imaginary numbers provide only an intermediate and conceptual mathematical result but have no physical significance in engineering and physics applications. Circle True or False.

2. A complex number is most often used in real world applications to quantify what kind of physical variable:

a. one dimensional
b. two dimensional
c. provides a theoretical base, but cannot describe physical variables
d. three dimensional
e. only variables describing particles smaller than an atom

3. In a vibration system with an oscillating input motion and an oscillating output motion, the imaginary part of a complex output can best be described as:

a. the part of the output that is unmeasureable
b. the part of the output that is negative
c. the component of the output that is negative but has a positive slope (increasing)
d. the component of the output that is quarter cycle ahead of the input
e. the component of the output that is in phase (peaks and valleys align) with the input

4. In a vibration system with an oscillating input motion and an oscillating output motion, the real part of a complex output can best be described as:

a. the part of the output that is unmeasureable
b. the part of the output that is positive
c. the component of the output that is positive but has a negative slope (decreasing)
d. the component of the output that is quarter cycle ahead of the input
e. the component of the output that is in phase (peaks and valleys align) with the input

And another variation on the test above:

1. Imaginary numbers are far more than a mathematical abstraction; they often represent physical characteristics in engineering and physics applications. Circle True or False.

2. A complex number is most often used in real world applications to quantify what kind of physical variable:

a. one dimensional
b. provides a theoretical base, but cannot describe physical variables
c. three dimensional
d. only variables describing particles smaller than an atom
e. two dimensional

3. In a vibration system with an oscillating input motion and an oscillating output motion, the imaginary part of a complex output can best be described as:

a. the part of the output that is unmeasureable
b. the part of the output that is negative
c. the component of the output that is quarter cycle ahead of the input
d. the component of the output that is in phase (peaks and valleys align) with the input
e. the component of the output that is negative but has a positive slope (increasing)

4. In a vibration system with an oscillating input motion and an oscillating output motion, the real part of a complex output can best be described as:

a. the part of the output that is positive
b. the component of the output that is positive but has a negative slope (decreasing)
c. the component of the output that is quarter cycle ahead of the input
d. the component of the output that is in phase (peaks and valleys align) with the input
e. the part of the output that is unmeasureable

Comments Welcome!


3 Responses to “Quiz for Applications of Imaginary Numbers”

  1. icecream4god Says:

    This is awesome. Thanks!

  2. Richard Conant Says:

    If you have a circuit with R, L, C denoting Resistance, Inductance and Capacitance, where generally R is independent of frequency, C impedance decreases with increased frequency and L impedance increases with increased frequency. Then i which can become + which is comprehensible or root(-1) which remains incomprehensible and can be thought of as vectors which add or subtract as do vectors. Imaginary numbers are widely used in Electrical theory and what else?

  3. adem muhidin Says:

    hi it is important for me ok