MCQ
The remainder when $7^{2022}+3^{2022}$ is divided by 5 is.
- A$0$
- B$2$
- ✓$3$
- D$4$
$=(49)^{1011}+(9)^{1011}$
$=(50-1)^{1011}+(10-1)^{1011}$
$=5 \lambda-1+5 K -1$
$=5\,m -2$
Remainder $=5-2=3$
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$\mathrm{S}_{1}=\{\mathrm{z} \in \mathrm{C}:|\mathrm{z}-2| \leq 1\} \text { and }$
$\mathrm{S}_{2}=\{\mathrm{z} \in \mathrm{C}: \mathrm{z}(1+\mathrm{i})+\overline{\mathrm{z}}(1-\mathrm{i}) \geq 4\}$
Then, the maximum value of $\left|z-\frac{5}{2}\right|^{2}$ for $z \in \mathrm{S}_{1} \cap \mathrm{S}_{2}$ is equal to: