Let zinmathbb C with operatornameIm(z)=10 and it satisfies (2z-n)/(2z+n)=2i-1 for some natural number n . Then

Complex Numbers: Let zinmathbb C with operatornameIm(z)=10 and it satisfies… | JEE Main 2019

JEE Main 2019 (Online) 12th April Evening ShiftQuestion 1

Let $z\in\mathbb C$ with $\operatorname{Im}(z)=10$ and it satisfies $\frac{2z-n}{2z+n}=2i-1$ for some natural number $n$. Then

Complex Numbers

$n=20$ and $\operatorname{Re}(z)=10$$n=40$ and $\operatorname{Re}(z)=10$$n=20$ and $\operatorname{Re}(z)=-10$$n=40$ and $\operatorname{Re}(z)=-10$✓ Correct answer

Solution

$2z-n=(2i-1)(2z+n)$ gives $z(4-4i)=2in$, so $z=\frac{n(i-1)}4$. $\operatorname{Im}z=\frac n4=10$ gives $n=40$ and $\operatorname{Re}z=-10$.

Complex Numbers - JEE Mathematics question (JEE Main 2019 (Online) 12th April Evening Shift)

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