Math Problem Statement

Plot the complex number -i - 3.

Solution

The complex number given is i3-i - 3, which can be rewritten as 3i-3 - i. To plot this on the complex plane:

  1. The real part of the complex number is 3-3, which corresponds to the horizontal axis (Real axis).
  2. The imaginary part is 1-1, which corresponds to the vertical axis (Imaginary axis).

To plot 3i-3 - i:

  • Start at the origin (0,0)(0, 0).
  • Move 3 units to the left (because the real part is 3-3).
  • Move 1 unit down (because the imaginary part is 1-1).

So, the point to plot is at (3,1)(-3, -1) on the complex plane.

Would you like any further details or explanations? Here are some related questions for further exploration:

  1. What is the geometric interpretation of the magnitude of a complex number?
  2. How do you determine the angle (argument) of a complex number on the complex plane?
  3. How would you plot the complex conjugate of 3i-3 - i?
  4. What does it mean to add two complex numbers graphically?
  5. How can you multiply two complex numbers geometrically?

Tip: The horizontal axis represents the real part, and the vertical axis represents the imaginary part when plotting complex numbers.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Coordinate Plane

Formulas

Complex number representation: a + bi

Theorems

Plotting complex numbers on the complex plane

Suitable Grade Level

Grades 9-12