SOLUTION: Write the complex number in the form a + bi. five divided by two(cos 150° + i sin 150°)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Write the complex number in the form a + bi. five divided by two(cos 150° + i sin 150°)       Log On


   

Question 973493: Write the complex number in the form a + bi.
five divided by two(cos 150° + i sin 150°)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Is this it?
+5+%2F+%28+2%2A%28+cos%28150%29+%2B+i%2Asin%28150%29+%29+%29+
++150+=+180+-+30+
so, 150 degrees is in the 2nd quadrant and makes
a 30 degree angle with the negative x-axis
+cos%28+150+%29+=+-sqrt%283%29+%2F+2+
+sin%28+150+%29+=+1%2F2+
---------------------
Now I have:
+5+%2F+%28+2%2A%28+-sqrt%283%29%2F2+%2B+i%2F2+%29%29+
------------------------------------
+5+%2F+%28+sqrt%283%29+%2B+i+%29+
----------------------
Multiply top and bottom by +sqrt%283%29+-+i+
------------------------------------------

-----------------------------------------------
+%28+5%2A%28+sqrt%283%29+-+i+%29%29+%2F+%28+3+%2B+1+%29+
--------------------------------
+%28+5%2F4%29%2Asqrt%283%29+-+%285%2F4%29%2Ai+
-----------------------------
Hope I got it -check my math