SOLUTION: Simplify 2i + 5 ______ 3i - 4 to the form ai + b. Express z = -2 -5i in polar form. Express z = 3 + 5i in exponential form. Use De Moivre's

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Simplify 2i + 5 ______ 3i - 4 to the form ai + b. Express z = -2 -5i in polar form. Express z = 3 + 5i in exponential form. Use De Moivre's       Log On


   

Question 550679: Simplify
2i + 5
______

3i - 4
to the form ai + b.




Express z = -2 -5i in polar form.



Express z = 3 + 5i in exponential form.


Use De Moivre's Theorem to express cos4 0 as powers of cos0.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify
2i + 5
______

3i - 4
to the form ai + b.
----------------
(2i + 5)/(3i - 4)
Multiply by the conjugate of the DEN
= (2i + 5)*(3i + 4)/((3i - 4)*3i + 4))
= (6i^2 + 20 + 23i) / (9i^2 - 16)
= (-6 + 20 + 23i) / (-9 - 16)
= (14 + 23i)/(-25)
= (-14/25) - (23/25)i
---------------------------
Express z = -2 -5i in polar form.
r+=+sqrt%282%5E2+%2B+5%5E2%29+=+sqrt%2829%29
Angle = arctan(-2/-5) = arctan(0.4)
Angle =~ 21.8 degs in Q3 --> 201.8 degs = 3.522 radians
--> (sqrt(29),3.522)
---------------------
Express z = 3 + 5i in exponential form.


Use De Moivre's Theorem to express cos4 0 as powers of cos0.