Math Problem Statement

Write the following numbers in exponential form: 2 + 2√3i og 1 − i. Draw them into the complex plane.

Solution

Here is the plot of the complex numbers 2+23i2 + 2\sqrt{3}i (in blue) and 1i1 - i (in red) on the complex plane:

  • The blue point represents 2+23i2 + 2\sqrt{3}i, which lies at (2,23)(2, 2\sqrt{3}) and makes an angle of π3\frac{\pi}{3} with the positive real axis.
  • The red point represents 1i1 - i, which lies at (1,1)(1, -1) and makes an angle of π4-\frac{\pi}{4} with the positive real axis.

Would you like further details or have any questions?

Related Questions:

  1. How do you convert a complex number from exponential form to standard form?
  2. What are the polar coordinates of the complex number 3+4i3 + 4i?
  3. How do you find the conjugate of a complex number in exponential form?
  4. What is the geometric interpretation of multiplying two complex numbers?
  5. How do you calculate powers of complex numbers using exponential form?

Tip:

When working with complex numbers in exponential form, the magnitude represents the distance from the origin, and the argument represents the angle from the positive real axis.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Complex Numbers
Exponential Form
Polar Coordinates
Complex Plane

Formulas

Exponential form of a complex number: z = r(cos(θ) + i sin(θ)) or z = re^(iθ)
Magnitude of a complex number: |z| = √(a^2 + b^2) for z = a + bi
Argument of a complex number: θ = atan2(b, a) for z = a + bi

Theorems

Euler's Formula
Polar Representation of Complex Numbers

Suitable Grade Level

Grades 10-12