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If $\mathrm{z}_{1}$ and $\mathrm{z}_{2}$ are complex numbers with $\left|\mathrm{z}_{1}\right|=\left|\mathrm{z}_{2}\right|$, then which of the following is/are correct?
1- $z_{1}=z_{2}$
2- Real part of $\mathrm{z}_{1}=$ Real part of $\mathrm{z}_{2}$
3- Imaginary part of $z_{1}=$ Imaginary part of $z_{2}$ Select the correct answer using the code given below:
Options:
1- $z_{1}=z_{2}$
2- Real part of $\mathrm{z}_{1}=$ Real part of $\mathrm{z}_{2}$
3- Imaginary part of $z_{1}=$ Imaginary part of $z_{2}$ Select the correct answer using the code given below:
Solution:
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Verified Answer
The correct answer is:
None
Let $Z_{1}=a_{1}+i b_{1}$ $\mathrm{Z}_{2}=\mathrm{a}_{2}+\mathrm{ib}_{2}$
$\left|\mathrm{Z}_{1}\right|=\left|\mathrm{Z}_{2}\right|$
$\sqrt{\left(\mathrm{a}_{1}\right)^{2}+\left(\mathrm{b}_{1}\right)^{2}}=\sqrt{\left(\mathrm{a}_{2}\right)^{2}+\left(\mathrm{b}_{2}\right)^{2}}$
It is true for many values of $\mathrm{a}_{1}, \mathrm{a}_{2} \& \mathrm{~b}_{1}, \mathrm{~b}_{2}$. So $\mathrm{a}_{1}$ must not equal to $\mathrm{a}_{2}$, and $\mathrm{b}_{1}$ must not equal to $\mathrm{b}_{2}$.
$\left|\mathrm{Z}_{1}\right|=\left|\mathrm{Z}_{2}\right|$
$\sqrt{\left(\mathrm{a}_{1}\right)^{2}+\left(\mathrm{b}_{1}\right)^{2}}=\sqrt{\left(\mathrm{a}_{2}\right)^{2}+\left(\mathrm{b}_{2}\right)^{2}}$
It is true for many values of $\mathrm{a}_{1}, \mathrm{a}_{2} \& \mathrm{~b}_{1}, \mathrm{~b}_{2}$. So $\mathrm{a}_{1}$ must not equal to $\mathrm{a}_{2}$, and $\mathrm{b}_{1}$ must not equal to $\mathrm{b}_{2}$.
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