Let z be a complex number with non-zero imaginary part. If 2 + 3 z + 4 z 2 2 - 3 z + 4 z 2 is a real number, then the value of z 2 is ______.

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Aicharya · Accepted Answer

Let &#945; = 4 z 2 + 3 z + 2 4 z 2 - 3 z + 2 = 1 + 6 z 4 z 2 - 3 z + 2 &#8658; &#160; &#945; = 1 + 6 2 2 z + 1 z - 3 &#8757; &#160; &#945; &#8712; R then 2 z + 1 z &#8712; R &#8658; 2 z + 1 z = 2 z &#175; + 1 z &#175; &#8658; 2 z - z &#175; - z - z &#175; z 2 = 0 &#8658; z - z &#175; 2 - 1 z 2 = 0 &#8757; &#160; z &#8800; z &#175; (given) So z 2 = 1 2 = 0 . 5

Let z be a complex number with non-zero imaginary part. If 2 + 3 z + 4 z 2 2 - 3 z + 4 z 2 is a real number,…

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