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Question Number 140444 by EnterUsername last updated on 07/May/21

$$\mathrm{If}\mathrm{the}\mathrm{points}1+2i\mathrm{and}-1+4i\mathrm{are}\mathrm{reflections}\mathrm{of}$$$$\mathrm{each}\mathrm{other}\mathrm{in}\mathrm{the}\mathrm{line}z(1+i)+\overline{z}(1-i)+K=0,\mathrm{then}$$$$\mathrm{the}\mathrm{value}\mathrm{of}K\mathrm{is}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}.$$

Answered by mr W last updated on 08/May/21

$$midpointfrom1+2iand-1+4iis3i,$$$$whichliesontheline.$$$$z=3i,\overline{z}=-3i$$$$3i(1+i)-3i(1-i)+k=0$$$$3i-3-3i-3+k=0$$$$\Rightarrow k=6$$

Commented by EnterUsername last updated on 12/May/21

$$\mathrm{Thanks}$$

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