Write the complex number in trigonometric form using degrees. -4 + 4i
A) 4 (cos 45° + i sin 45°)
B) 32(cos 45° + i sin 45°)
C) 4 (cos 135° + i sin 135°)
D) 32(cos 135° + i sin 135°)

Question

Write the complex number in trigonometric form using degrees. -4 + 4i
A) 4 (cos 45° + i sin 45°) 
B) 32(cos 45° + i sin 45°) 
C) 4 (cos 135° + i sin 135°) 
D) 32(cos 135° + i sin 135°)

Quizplus · Accepted Answer

To convert the complex number -4 + 4i to trigonometric form, we need to find its magnitude (r) and angle in standard position (θ). Magnitude can be found using the Pythagorean theorem: r = √((-4)^2 + 4^2) = 4√2. The angle can be found using the inverse tangent function: θ = tan⁻¹(4/-4) = 135°. Therefore, the complex number can be expressed as 4√2(cos 135° + i sin 135°), which matches choice C.

Write the Complex Number in Trigonometric Form Using Degrees