Expert: Paul Klarreich - 8/31/2011

Question
Find real values of x for which (4+3isinx/1-2isinx) is purely
1)real
2)purely imaginary

Answer
Questioner:Dhananjay
Country:Maharashtra, India
Category:Advanced Math
Private:No
Subject:Complex number

Question:

Find real values of x for which (4+3isinx/1-2isinx) is purely
1)real
2)purely imaginary
.............................
I assume you meant:

(4+3isinx )  / (  1-2isinx)
Suppose we rationalize (always a good thing with complex division.)

4 + 3 i sinx  1 + 2 i sinx   
------------- ------------- =
1 - 2 i sinx  1 + 2 i sinx

4 - 6 sin^2 x + 11 i sin x
-------------------------- =
1 + 4 sin^2 x

Now, since the denominator is real, you will have an expression that is:

1)real

if  11 i sin x = 0

So you have a trigonometric equation to solve.

2)purely imaginary

if  4 - 6 sin^2 x = 0

So you have another trigonometric equation to solve.

You can finish this up.  See past answers with subject line:

Trigonometric Equation.