COMEDK 2026 Afternoon Shift | Complex Numbers Question 1 | Mathematics

The conjugate of the multiplicative inverse of the complex number $\boldsymbol{z}=\frac{\mathbf{1}+\mathbf{7} \boldsymbol{i}}{\mathbf{3}+\boldsymbol{i}}$ is:

$\frac{2}{5}+\frac{1}{5} i$

$\frac{1}{5}-\frac{2}{5} i$

$\frac{1}{5}+\frac{2}{5} i$

$1+2 i$

COMEDK 2026 Morning Shift

MCQ (Single Correct Answer)

-0

$$ \text { The conjugate of } z=\frac{(\mathbf{4}+\boldsymbol{i})(\mathbf{1}-\boldsymbol{i})}{(\mathbf{1}+\boldsymbol{i})(\mathbf{2}-\boldsymbol{i})} $$

$\frac{6}{5}+\frac{7}{5} i$

$\frac{1}{2}-\frac{1}{2} i$

$\frac{6}{5}-\frac{7}{5} i$

$\frac{1}{2}+\frac{1}{2} i$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

Given that $z$ is a real number and $z=\frac{\lambda+4 i}{1+\lambda i}$ where $\lambda \in R$, then the possible value of $\lambda$ is :

$-2$

$2 i$

$5$

$\pm 2 i$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

If $z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5$, then

$\operatorname{Re}(z)>0, \operatorname{Im}(z)<0$

$\operatorname{Im}(z)=0$

$\operatorname{Re}(z)=0$

$\operatorname{Re}(z)>0, \operatorname{Im}(z)>0$

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