Let A = θ ∈ - π 2 , π : 3 + 2 i   s i n θ 1 - 2 i   s i n θ   i s   p u r e l y   i m a g i n a r y   . Then the sum of the elements in A is:

Question

Let A = &#952; &#8712; - &#960; 2 , &#960; : 3 + 2 i &#8201; s i n &#952; 1 - 2 i &#160; s i n &#952; &#160; i s &#160; p u r e l y &#160; i m a g i n a r y &#160; . Then the sum of the elements in A is:

Aicharya · Accepted Answer

Given complex number is z = 3 + 2 i s i n θ 1 - 2 i s i n θ ⇒ z = ( 3 + 2 i s i n θ ) ( 1 + 2 i s i n θ ) ( 1 + 4 s i n 2 θ ) Since given complex number is purely imaginary ⇒ R e ( z ) = 0 ⇒ 3 - 4 s i n 2 θ = 0 ⇒ s i n θ = ± 3 2 ⇒ θ = - π 3 , π 3 , 2 π 3 ⇒ sum of all possible values of θ = 2 π 3 .

Let A = θ ∈ - π 2 , π : 3 + 2 i   s i n θ 1 - 2 i   s i n θ  …

Solution

Let A = &#952; &#8712; - &#960; 2 , &#960; : 3 + 2 i &#8201; s i n &#952; 1 - 2 i &#160; s i n &#952; &#160;…

Solution

Let A = θ ∈ - π 2 , π : 3 + 2 i s i n θ 1 - 2 i s i n θ …