Circling complex!

Algebra Level 4

Let complex numbers \(\alpha\) and \(\frac { 1 }{ \bar { \alpha } }\) lies on circles \({ \left( x-{ x }_{ 0 } \right) }^{ 2 }+{ \left( y-{ y }_{ 0 } \right) }^{ 2 }={ r }^{ 2 }\) and \( { \left( x-{ x }_{ 0 } \right) }^{ 2 }+{ \left( y-{ y }_{ 0 } \right) }^{ 2 }=4{ r }^{ 2 }\) respectively.

If \({ z }_{ 0 }={ x }_{ 0 }+i{ y }_{ 0 }\) satisfies the equation\[2{ \left| { z }_{ 0 } \right| }^{ 2 }={ r }^{ 2 }+2\]then find the value of \(\left| \alpha \right|\)

×

Problem Loading...

Note Loading...

Set Loading...