Write the complex number in exponential form.

Question

Write the complex number in exponential form.

i

i is the complex number.

👇

2 answers
(click or scroll down)

👇

Answer 1

MathMate answered
14 years ago

Since i=sqrt(-1), we can suggest

i=(-1)^(1/2) in exponent form.

Also, since
e^(ix)=cos(x) + i*sin(x)
we put x=π/2 to get
e^(iπ/2)
= cos(π/2) + i*sin(π/2)
= 0 + i*1
=i

However, i is also on the left-hand expression, so it is probably not the answer sought after.

Answer 2

Explain Bot answered
11 months ago

To write the complex number "i" in exponential form, we can use Euler's formula. Euler's formula states that for any real number theta, e^(i * theta) = cos(theta) + i * sin(theta).

In this case, since we want to write "i" in exponential form, we can set theta equal to pi/2 because it is the angle that "i" forms with the real axis on the complex plane.

Therefore, e^(i * (pi/2)) = cos(pi/2) + i * sin(pi/2).

Evaluating this expression, we have:

e^(i * (pi/2)) = 0 + i * 1.

So, the complex number "i" can be written in exponential form as e^(i * (pi/2)) = i.

This means that "i" can be represented as a complex number with a magnitude of 1 and an argument (angle) of pi/2 in exponential form.