SOLUTION: Heya, I'd be really greatful if you could solve this question from calculus, complex numbers for me. Find the complex number u = x + yi, where x and y are real numbers, so that

When we solve this quadratic equation:



by the quadratic formula and simplify, we get this:

 

To simplify further we need to find a simpler form for
the square root, say u = x + yi such that



Squaring both sides:









Set real parts equal:



Set imaginary parts equal:





Solve system:



Solve the second for a letter , substitute it in the first,

and get two solutions (x,y) = (2,3) and (x,y) = (-2,-3).

So  which can either be 2+3i or -2-3i.

Thus 

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So the solution to



which was:



becomes



Using the +, that simplifies to 1+i

Using the -, that simplifies to -1-2i

So those are the two solutions to the quadratic.

Edwin