Let complex numbers α and lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 =

Question

Let complex numbers &#945; and lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2 respectively. If z0 = x0 + iy0 satisfies the equation 2|z0|2 = r2 + 2, then |&#945;| =

Accepted Answer

Given : &#945; satisfies |z - z0| = r &#8658; |&#945; - z0 | = r ..........(1) satisfies |z - z0| = 2r .........(2) squaring (1) and (2) we get &#8658; ..........(3)& &#8658; &#8658; &#8658; 1+ 2 |z0|2 - 2 - |&#945;|2 - |z0|2 + |z0|2 |&#945;|2 = 8|z0|2 |&#945;|2 - 8|&#945;|2&#8658; -1 + |z0|2 - 7|z0|2 |&#945;|2 + 7|&#945;|2 = 0&#8658; (|z0|2 - 1) (7|&#945;2|- 1) = 0&#8658; |z0| = 1 (rejected as r = 0)&

Question

Options

Solution

More Complex Numbers Questions