Question:
Give an example of two complex numbers $z_{1}$ and $z_{2}$ such that $z_{1} \neq z_{2}$ and $\left|z_{1}\right|=$ $\left|\mathbf{z}_{2}\right| .$
Solution:
Let $z_{1}=3-4 i$ and $z_{2}=4-3 i$
Here, $z_{1} \neq z_{2}$
Now, calculating the modulus, we get,
$\left|z_{1}\right|=\sqrt{3^{2}+(4)^{2}}=\sqrt{25}=5$
$\left|z_{2}\right|=\sqrt{4^{2}+(3)^{2}}=\sqrt{25}=5$