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 ·Oct 13 '13 at 23:02

Let

$a = x + i y, z = m i$

Substitute these values in the equation.

$(- x m 2 + 1) + i (- m 2 y + m) = 0$

$\to x = y 2 $

$∣ a ∣ = 1$
$\to x 2 + y 2 = 1$
$\to x 2 + x - 1 = 0$
$\to x = 2 - 1 \pm \sqrt 5 $

x>0 since y has to be real.

$x = 2 \sqrt 5 - 1 y = \sqrt 2 \sqrt 5 - 1 $

341

Hari Shankar ·Oct 12 '13 at 22:46

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

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