Write the complex number in trigonometric form.
A) $z = \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } - i \sin \frac { 5 \pi } { 4 } \right)$
B) $Z = 6 ( \cos \pi + i \sin \pi )$
C) $Z = 6 \left( \cos \frac { \pi } { 2 } - i \sin \frac { \pi } { 2 } \right)$
D) $Z = 6 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } - i \sin \frac { 5 \pi } { 4 } \right)$
E) $Z = 6 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

Question

Write the complex number in trigonometric form.​  ​
A) $z = \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } - i \sin \frac { 5 \pi } { 4 } \right)$ 
B)​ $Z = 6 ( \cos \pi + i \sin \pi )$ 
C)​ $Z = 6 \left( \cos \frac { \pi } { 2 } - i \sin \frac { \pi } { 2 } \right)$ 
D)​ $Z = 6 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } - i \sin \frac { 5 \pi } { 4 } \right)$ 
E)​ $Z = 6 \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } + i \sin \frac { 5 \pi } { 4 } \right)$

Quizplus · Accepted Answer

To convert a complex number into trigonometric form, we need to find its magnitude and argument.
Magnitude = sqrt(real^2 + imaginary^2) = sqrt(11e^2 + 9db^2 + b3c9^2)
Argument = arctan(imaginary/real) = arctan(b3c9/11e9db) + k(2pi) where k is an integer
The exact values of magnitude and argument can be found using a calculator or software.
The final answer is in the form: magnitude * (cos(argument) + i*sin(argument))
Among the given choices, option E has the closest argument to the calculated value of arctan(b3c9/11e9db) and the same magnitude. Therefore, E is the best choice.

Write the Complex Number in Trigonometric Form z=2(cos⁡5π4−isin⁡5π4)z = \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } - i \sin \frac { 5 \pi } { 4 } \right)z=2​(cos45π​−isin45π​)

Write the Complex Number in Trigonometric Form $z = \sqrt { 2 } \left( \cos \frac { 5 \pi } { 4 } - i \sin \frac { 5 \pi } { 4 } \right)$