Find the argument of the complex number minus, 5, plus, 4, i−5+4i in the interval 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , rounding to the nearest tenth of a degree if necessary.

The argument of a complex number is the angle it makes with the positive real axis.

The complex number in question is -5 + 4i.

We can find the argument (θ) using the formula θ = atan2(b, a), where a is the real part of the number and b is the imaginary part.

In this case, a = -5 and b = 4.

So, θ = atan2(4, -5).

This will give us the angle in radians. To convert to degrees, we multiply by 180/π.

However, the atan2 function gives a result in the range -π to π, or -180° to 180°. Since we want a result in the range 0° to 360°, if the result is negative, we add 360°.

So, the argument of the complex number -5 + 4i is θ = atan2(4, -5) * 180/π. If θ is negative, add 360°.

Finally, round to the nearest tenth of a degree if necessary.

The argument of a complex number is the angle it makes with the positive real axis.

The complex number in question is -5 + 4i.

We can find the argument (θ) using the formula θ = atan2(b, a), where a is the real part of the number and b is the imaginary part.

In this case, a = -5 and b = 4.

So, θ = atan2(4, -5).

This will give us an angle in radians, which is negative because the complex number is in the second quadrant.

To convert this to degrees, we multiply by 180/π.

Finally, because we want the angle in the range 0° ≤ θ < 360°, we add 360° to the result if it's negative.

So, the argument of the complex number -5 + 4i is approximately 141.4° when rounded to the nearest tenth of a degree.

The complex number in question is -5 + 4i.

Step 1: Convert the complex number to polar form. The polar form of a complex number is r(cos θ + i sin θ), where r is the magnitude of the complex number and θ is the argument of the complex number.

Step 2: Calculate the magnitude r. The magnitude r of a complex number a + bi is given by √(a² + b²). So, r = √((-5)² + 4²) = √41.

Step 3: Calculate the argument θ. The argument θ of a complex number a + bi is given by tan⁻¹(b/a). However, because a is negative in this case, we need to add 180° to the result to get the argument in the correct quadrant. So, θ = tan⁻¹(4/-5) + 180° = -38.7° + 180° = 141.3°.

So, the argument of the complex number -5 + 4i in the interval 0° ≤ θ < 360° is 141.3°, rounded to the nearest tenth of a degree.