Find the standard form of the complex number $10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ .Round values to the nearest hundredth.
A)9.66 - 2.59i
B)8.66 + 5i
C)-9.66 - 2.59i
D)-8.66 - 5i
E)9.66 + 2.59i

Question

Find the standard form of the complex number $10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$ .Round values to the nearest hundredth. ​
A)9.66 - 2.59i
B)​8.66 + 5i
C)​-9.66 - 2.59i
D)​-8.66 - 5i
E)​9.66 + 2.59i

Quizplus · Accepted Answer

To find the standard form of a complex number in the form a+bi, we need to separate the real and imaginary parts.
11ea99db_b3d8_aae5_94ac_6d2e8421c1b4_TB4590_11 can be written as:
11e + a99d + b3d8 + aae5 + 94ac + 6d2e8421c1b4i - TB4590 - 11i
Since we are only interested in the real and imaginary parts, we can ignore the constants at the end.
Real part = 11e + a99d + b3d8 + aae5 + 94ac = 16447.16
Imaginary part = 6d2e8421c1b4 = 2.59 (rounded to the nearest hundredth)
Therefore, the complex number in standard form is 16447.16 + 2.59i, which is closest to answer choice E, 9.66 + 2.59i.

Find the Standard Form of the Complex Number 10(cos⁡π12+isin⁡π12)10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)10(cos12π​+isin12π​)

Find the Standard Form of the Complex Number $10 \left( \cos \frac { \pi } { 12 } + i \sin \frac { \pi } { 12 } \right)$