Question

Use Euler's formula to write -10 sqrt3 +10i; in exponential form?

Answer 1

To write -10 sqrt3 +10i in exponential form using Euler's formula, we need to determine the magnitude and argument of the complex number. The magnitude can be found using the Pythagorean theorem and the argument can be determined using the inverse tangent function.

Step-by-step explanation:

To write -10√3 +10i in exponential form using Euler's formula, we need to identify the magnitude (r) and argument (θ) of the complex number.

The magnitude can be found using the Pythagorean theorem:

|z| = sqrt((-10√3)^2 + (10)^2) = sqrt(300+100) = sqrt(400) = 20

The argument can be determined using the inverse tangent function:

θ = arctan(10/(-10√3)) = arctan(-1/√3) = -π/6

Therefore, -10√3 +10i can be written in exponential form as 20( cos(-π/6) + i sin(-π/6) ).