Write -1-i in exponential form.
r= (-1)^2 + (-1)^2
sqrt2
1.4
e^1.4
To write -1-i in exponential form, we need to express it in the form r*e^(θi), where r is the magnitude of the complex number and θ is the argument (or angle) of the complex number.
First, we need to find the magnitude, r, which can be calculated using the formula r = sqrt(a^2 + b^2), where a is the real part (-1 in this case) and b is the imaginary part (-1 in this case).
So, r = sqrt((-1)^2 + (-1)^2) = sqrt(1 + 1) = sqrt(2).
Next, we need to find the argument, θ. The argument can be calculated as θ = arctan(b/a), where b is the imaginary part (-1) and a is the real part (-1).
So, θ = arctan(-1/-1) = arctan(1) = π/4.
Now, we can write -1-i in exponential form:
-1-i = sqrt(2) * e^(π/4 * i)
Therefore, the exponential form of -1-i is sqrt(2) * e^(π/4 * i).