The equation I m i z - 2 z - i + 1 = 0 ,   z ∈ C ,   z ≠ i represents a part of a circle having radius equal to :

Question

The equation I m i z - 2 z - i + 1 = 0 , &#160; z &#8712; C , &#160; z &#8800; i represents a part of a circle having radius equal to :

Aicharya · Accepted Answer

Let z = x + i y , then I m &#160; i x - y - 2 x + y - 1 i &#160; x - y - 1 i x - y - 1 i + 1 = y - 1 &#160; y + 2 + x 2 x 2 + y - 1 2 + 1 = 0 &#8658; 2 x 2 + 2 y 2 - y - 1 = 0 &#8658; x 2 + y 2 - y 2 - 1 2 = 0 Center ( 0 , &#160; 1 4 ) Radius = g 2 + f 2 - c Radius = &#160; 1 16 + 1 2 = &#160; 9 16 = 3 4

The equation I m i z - 2 z - i + 1 = 0 ,   z ∈ C ,   z ≠ i represents a part of a…

Solution

The equation I m i z - 2 z - i + 1 = 0 , &#160; z &#8712; C , &#160; z &#8800; i represents a part of a…

Solution

The equation I m i z - 2 z - i + 1 = 0 , z ∈ C , z ≠ i represents a part of a…