Question

The two complex numbers satisfying the equation $z\overline{z}-(1+i)z-(3+2i)\overline{z}+(1+5i)=0$ are

• A. $1+i,3+2i$
• B. $1+i,3-2i$
• C. $1-i,3+2i$
• D. $1-i,3-2i$

Answer 1

The correct option is C $1-i,3+2i$

Put $a=1+i,b=3+2i$

Then $ab=1+5i$

$\therefore z\overline{z}-az-b\overline{z}+ab=0$

$(\overline{z}-a)(z-b)=0$

$\therefore \overline{z}=a,z=b\text{or}z=\overline{a},z=b$

$z=1-i,3+2i$