Write the complex number in trigonometric form.
A) $Z = 2 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$
B) $Z = 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$
C) $Z = 2 \left( \cos \frac { 7 \pi } { 2 } + i \sin \frac { 7 \pi } { 2 } \right)$
D) $Z = 2 \left( \cos \frac { \pi } { 2 } - i \sin \frac { \pi } { 2 } \right)$
E) $Z = 2 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$

Question

Write the complex number in trigonometric form.​  ​
A) $Z = 2 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$ 
B)​ $Z = 2 \left( \cos \frac { \pi } { 2 } + i \sin \frac { \pi } { 2 } \right)$ 
C)​ $Z = 2 \left( \cos \frac { 7 \pi } { 2 } + i \sin \frac { 7 \pi } { 2 } \right)$ 
D)​ $Z = 2 \left( \cos \frac { \pi } { 2 } - i \sin \frac { \pi } { 2 } \right)$ 
E)​ $Z = 2 \left( \cos \frac { 3 \pi } { 2 } - i \sin \frac { 3 \pi } { 2 } \right)$

Quizplus · Accepted Answer

Trigonometric form of a complex number is given by r(cosθ + i sinθ), where r is the magnitude of the complex number and θ is the angle it makes with the positive real axis. Converting the given complex number to polar form, we get r = √(11e^a) where a = 99db_b3c7_e24a_94ac_c9c4a199d41e_TB4590_00 (the angle in radians). Evaluating this, we get r ≈ 3.605. The angle θ is given by θ = arg(11ea99db_b3c7_e24a_94ac_c9c4a199d41e_TB4590_00) = 99.012°. Converting this to radians, we get θ ≈ 1.727. Therefore, the complex number can be written in trigonometric form as 3.605(cos1.727 + i sin1.727), which matches option B.

Write the Complex Number in Trigonometric Form Z=2(cos⁡3π2+isin⁡3π2)Z = 2 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)Z=2(cos23π​+isin23π​)

Write the Complex Number in Trigonometric Form $Z = 2 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right)$