SOLUTION: Use DeMoivre's theorem to write in trigonometric from: (1/2 - i(√3)/2)

Algebra.Com
Question 1039836: Use DeMoivre's theorem to write in trigonometric from:
(1/2 - i(√3)/2)
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

The complex number  is represented by
the vector (arrow) from the origin to the point. Its length
is r and its angle with the right side of the x-axis is q.





We draw a perpendicular (in green) from the point to the
x-axis:



That makes a right triangle and we can use the
Pythagorean theorem:







And since we know that ,


 

So the trigonometric form of  

is  or



Or if yout teacher wants you to use radians, then 



.

Edwin
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
For lessons on complex numbers in this site see
    - Complex numbers and arithmetical operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
    - Raising a complex number to an integer power
    - How to take a root of a complex number
    - Solution of the quadratic equation with real coefficients on complex domain
    - How to take a square root of a complex number
    - Solution of the quadratic equation with complex coefficients on complex domain


RELATED QUESTIONS

Apply DeMoivre's Theorem and leave the result in trigonometric form (2 + 2i)^6 (answered by ikleyn)
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the... (answered by mccravyedwin)
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the... (answered by Edwin McCravy)
Use Demoivre's theorem to prove that... (answered by AnlytcPhil)
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the... (answered by Alan3354)
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the... (answered by AnlytcPhil)
Use DeMoivre’s theorem to find z4, if z is 1 + 1i. Express your answer in complex... (answered by Fombitz)
Use DeMoivre's theorem to write [3cis(pi/2)]^2 in the form a + bi without trigonometric... (answered by stanbon)
A 48-foot ladder resting against a house reaches a windowsill 32 feet above the ground.... (answered by Boreal)