Trigonometric Functions and Complex Numbers

Trigonometric Functions and Complex Numbers

Assessment

Interactive Video

Mathematics

11th - 12th Grade

Practice Problem

Hard

Created by

Jackson Turner

FREE Resource

The video tutorial explains how to use De Moivre's Theorem to work with complex numbers. It begins by identifying clues that suggest the use of the theorem, then demonstrates converting complex numbers from rectangular to polar form. The tutorial continues by applying De Moivre's Theorem to raise complex numbers to a power and concludes with simplifying expressions using symmetry properties of trigonometric functions.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a key indicator in the problem statement that suggests using De Moivre's Theorem?

The use of logarithms

The presence of a quadratic equation

The presence of a matrix

The angle is multiplied by n

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it necessary to convert complex numbers to polar form before applying De Moivre's Theorem?

To simplify the addition of complex numbers

To make multiplication easier

To apply the theorem correctly

To find the roots of the equation

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the modulus of the complex number 1 + i?

i

1

2

√2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the argument of the complex number 1 + i in polar form?

π/2

π/4

3π/4

π

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the argument of the complex number 1 - i?

-π/2

π/4

π/2

-π/4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the symmetry of trigonometric functions help in simplifying expressions?

It allows for easier differentiation

It simplifies integration

It helps in solving linear equations

It allows for cancellation of terms

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the modulus when a complex number is raised to the nth power using De Moivre's Theorem?

It remains the same

It is raised to the nth power

It is divided by n

It is multiplied by n

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