Question

Find the argument of the complex number — 3+ 8i in the interval 0°<theta<360⁰, rounding to the nearest tenth of a degree if necessary

​

Answer 1

The argument is 290.6°

Explanation:

For a complex number:

Z = a + b*i

The argument is:

θ = Atan(b/a)

Where Atan(x) is the inverse function of the tangent function, such that:

Atan(tan(x)) = x

tan(Atan(x)) = x

In this case, we have the complex number:

Z = -3 + 8*i

The argument of this complex number will be:

θ = Atan(8/-3) = -69.4°

But we want 0°< θ <360⁰

Also, remember that the trigonometric functions have a periodicity of 360°

Then:

cos(θ + n*360°) = cos(θ)

With n integer.

This means that our angle is equivalent to:

-69.4° + 360° = 290.6°

Then the argument is 290.6°, this one is on the desired interval (0°, 360°)