Write the complex number in exponential form.
i
i is the complex number.
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.
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.