 Quandaries and Queries I have a question in solving a root of a complex number... Solve: Z2 = 3 - 4i Let z= x + yi Rewrite as (x + yi)2 = 3 - 4i Expand x2 +2xyi + y2i2 = 3 - 4i Simplify x2 - y2 + 2xyi = 3 - 4i real/imag parts x2 - y2 = 3 and 2xy = -4 xy = -2 Therefore y = -2/x Substitute y = -2/x into x2 - y2 = 3 giving x^2 - 4/x2 = 3 Multiply by x2 x^4 - 4 = 3x^2 Factor Roots **> x^4 - 3x^2 - 4 = 0 (x2 + 1) (x2 - 4) = 0 (x2 + 1) (x + 2) (x - 2) = 0 Given xy = -2 for x = 2 then y = -1 therefore z = 2 - i for x = -2 then y = 1 therefore z = -2 + i OK... the 2 solutions for z shown are indicated as correct in the text, but these are the onnly solutions given. What about the (x2 + 1) root found in the line marked '**>'? How do I deal with it? Is it not used because it does not have a real result? Have I made a mistake or procedural error? Thanks for you assistance, John (uncertain parent of secondary student) Hi John, Back in the third line when you write the complex number z as z= x + yi there is an assumption that x any y are real. The roots of x2 + 1 are not real and hence do not give extra solutions to your problem. Harley Go to Math Central