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Euler’s Formula

What is the result when e^iπ/4is evaluated using Euler's formula?

$\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}$

$\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}$

$-\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}$

What is the result when e^3iπ/2is evaluated using Euler's formula?

i

-i

1

Euler's formula is often used to represent complex numbers in what form?

Rectangular form

Exponential form

Trigonometric form

In Euler's formula, what does represent?

The base of the natural logarithm

The imaginary unit

The complex argument

Fill in the blank
e^ix =

coscosx+i sinsinx

sinsinx -i coscosx

sinsinx + coscosx

In Euler's formula, if e^ix is a complex number, what is the reciprocal of this number?

e^ix

e^-ix

e^x

Euler's formula is a special case of a more general mathematical principle known as what?

De Moivre's theorem

Taylor's theorem

Fermat's principle

What is the result when eⁱ⁰ is evaluated using Euler's formula?

1

2 i

Euler's formula can be used to express sinusoidal functions in terms of complex exponentials. What is the advantage of this representation?

Questions

Time

Score

Euler’s Formula

What is the result when eiπ/4 is evaluated using Euler's formula?

﻿12+i2\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}2​1​+2​i​﻿

﻿12−i2\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}2​1​−2​i​﻿

﻿−12+i2-\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}−2​1​+2​i​﻿

What is the result when e3iπ/2 is evaluated using Euler's formula?

i

-i

1

Euler's formula is often used to represent complex numbers in what form?

Rectangular form

Exponential form

Trigonometric form

In Euler's formula, what does represent?

The base of the natural logarithm

The imaginary unit

The complex argument

Fill in the blank eix =

coscosx+i sinsinx

sinsinx -i coscosx

sinsinx + coscosx

In Euler's formula, if eix is a complex number, what is the reciprocal of this number?

eix

e-ix

ex

Euler's formula is a special case of a more general mathematical principle known as what?

De Moivre's theorem

Taylor's theorem

Fermat's principle

What is the result when ei0 is evaluated using Euler's formula?

1

2

i

Euler's formula can be used to express sinusoidal functions in terms of complex exponentials. What is the advantage of this representation?

It simplifies calculus operations

It makes the functions periodic

It makes the functions periodic

What is real part of eπi/3?

2

1/2

1

Incorrect

Great!

What is the result when e^iπ/4is evaluated using Euler's formula?

$\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}$

$\frac{1}{\sqrt{2}}-\frac{i}{\sqrt{2}}$

$-\frac{1}{\sqrt{2}}+\frac{i}{\sqrt{2}}$

What is the result when e^3iπ/2is evaluated using Euler's formula?

Fill in the blank
e^ix =

In Euler's formula, if e^ix is a complex number, what is the reciprocal of this number?

e^ix

e^-ix

e^x

What is the result when eⁱ⁰ is evaluated using Euler's formula?

What is real part of e^π^i/3?