Math Problem Statement

x = 3-2i

Solution

The expression x=32ix = 3 - 2i represents a complex number in the form a+bia + bi, where a=3a = 3 is the real part and b=2b = -2 is the imaginary part.

Would you like to explore any specific properties of this complex number? Here are a few things we can discuss:

  1. Modulus (Magnitude) of xx
  2. Argument (Angle) of xx
  3. Converting xx to polar form
  4. Complex conjugate of xx
  5. Operations involving complex numbers, such as addition, multiplication, or division.

Do you want more details on any of these or have any questions?

Related questions:

  1. What is the modulus of the complex number 32i3 - 2i?
  2. How do you find the argument of a complex number?
  3. What is the complex conjugate of 32i3 - 2i?
  4. How do you convert a complex number to polar form?
  5. What is the result of adding two complex numbers like 32i3 - 2i and 4+5i4 + 5i?

Tip:

When dealing with complex numbers, always remember that the modulus represents the distance from the origin in the complex plane.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Complex Numbers
Algebra

Formulas

Modulus of a complex number: |z| = sqrt(a^2 + b^2)
Argument of a complex number: arg(z) = atan2(b, a)
Polar form of a complex number: z = |z|(cos θ + i sin θ)

Theorems

Pythagorean Theorem (used in calculating modulus)
Euler's Formula

Suitable Grade Level

Grades 10-12