Final answer:
To express -1+8i in the interval 0°≤θ<360°, the angle θ that corresponds to the complex number -1+8i can be found using the formula tan⁻¹(θ) = Im/Re. Adding 360° to the initial angle and then subtracting 360° if necessary will give us the angle within the desired interval. The angle θ is approximately 281.57°.
Step-by-step explanation:
To express -1+8i in the interval 0°≤θ<360°, we need to find the angle θ that corresponds to the complex number -1+8i. The angle can be found using the formula tan⁻¹(θ) = Im/Re, where Im is the imaginary part and Re is the real part of the complex number. In this case, Im = 8 and Re = -1. Using a calculator, we can find θ as approximately 281.57°. However, this angle is in the fourth quadrant, so we need to add 360° to obtain the angle in the interval 0°≤θ<360°. Adding 360° gives us approximately 641.57°. Since this angle is larger than 360°, we need to subtract 360° to get it within the desired interval. Substracting 360° gives us approximately 281.57°. Therefore, the angle θ that corresponds to -1+8i in the interval 0°≤θ<360° is approximately 281.57°.