Question

If $(x+iy{)}^5=p+iq$, then the value of $\frac{2(y+ix{)}^5}{q+ip}$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Given : $(x+iy{)}^5=p+iq$
Now,
$\frac{2(y+ix{)}^5}{q+ip}=\frac{2i^5(x-iy{)}^5}{i(p-iq)}=\frac{2(x-iy{)}^5}{(p-iq)}=\frac{2{\overline{(x+iy)}}^5}{\overline{(p+iq)}}=\frac{2\overline{(x+iy{)}^5}}{\overline{(p+iq)}}(\because (\overline{z^n})=(\overline{z}{)}^n)=2\overline{\left(\frac{(x+iy{)}^5}{p+iq}\right)}(\because \frac{\overline{z_1}}{\overline{z_2}}=\overline{\left(\frac{z_1}{z_2}\right)})=2\times 1=2$