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 (in blue) and (in red) on the complex plane:
- The blue point represents , which lies at and makes an angle of with the positive real axis.
- The red point represents , which lies at and makes an angle of with the positive real axis.
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Related Questions:
- How do you convert a complex number from exponential form to standard form?
- What are the polar coordinates of the complex number ?
- How do you find the conjugate of a complex number in exponential form?
- What is the geometric interpretation of multiplying two complex numbers?
- 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.
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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