Complex numbers

If 'a' is a complex number such that |a|=1.Find the values of a,so that equation az²+z+1=0 has one purely imaginary root.

2 Answers

2305

Shaswata Roy ·2013-10-13 23:02:29

Let

a=x+iy,z = mi

Substitute these values in the equation.

(-xm^2+1)+i(-m^2y+m)=0

\rightarrow x=y^2

|a|=1
\rightarrow x^2+y^2=1
\rightarrow x^2+x-1=0
\rightarrow x=\frac{-1\pm \sqrt{5}}{2}

x>0 since y has to be real.

x=\frac{\sqrt{5}-1}{2}\qquad y=\sqrt{\frac{\sqrt{5}-1}{2}}

341

Hari Shankar ·2013-10-12 22:46:44

http://goiit.com/posts/list/algebra-help-needed-in-a-question-of-complex-numbers-1199242.htm

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