## A bit challenging problem on complex numbers

**Problem:**

If and satisfy the equation

then find the value of .

**Solution:**

We can write the given equation as

This is a fourth degree equation whose two roots are . Let be the other two roots. Then,

(sum of the products taken two at a time)

or

Hence, we get .

Note that in deriving the fourth degree equation we used a basic technique of expansion or multiplication of several binomials.

More later,

Nalin Pithwa

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