JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q62

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MathematicsSingle correct+4 / -1Question 62 of 90

If $z$ is a non-real complex number, then the minimum value of $\dfrac{\text{Im }z^5}{(\text{Im }z)^5}$ is :

−1

−2

−4

−5

Answer and worked solution

Official answer: C

With $z=x+iy$ ( $y\ne0$ ) and $t=\frac{x^2}{y^2}\ge0$ :
$\frac{\text{Im }z^5}{y^5}=\frac{5x^4y-10x^2y^3+y^5}{y^5}=5t^2-10t+1.$
The minimum, at $t=1$ , is $-4$ .

Topics:Algebra of complex numbers Quadratic expressions

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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 62