If the points represented by complex numbers $$z1=a+ib$$,$$z2=c+id$$ and $$z1$$−$$z2$$ are collinear, where $$i=$$−$$1$$ then

Question

If the points represented by complex numbers $$z1=a+ib$$,$$z2=c+id$$  and  $$z1$$−$$z2$$  are collinear, where $$i=$$−$$1$$ then

Infinity Learn · Accepted Answer

Since,  $$z1$$,$$z2$$  and  $$z1$$−$$z2$$  are collinear∴ $$z1z$$¯$$11z2z$$¯$$21z1$$−$$z2z1$$−$$z2$$¯$$1=0$$                ⇒ $$z1z$$¯$$11z2z$$¯$$21z1$$−$$z2z$$¯$$1$$−z¯$$21=0Applying$$ $$R3$$→$$R3$$−$$R1+R2$$, then $$z1z$$¯$$11z2z$$¯$$21001$$   $$=0$$                                           $$z1z$$¯$$2$$−z¯$$1z2$$    $$=0$$⇒                    $$z1z$$¯$$2$$−z $$1z$$¯$$2$$    $$=0$$⇒                        Im⁡$$z1z$$¯$$2$$    $$=0$$⇒                          ⇒                            Im⁡$$((a+ib)(c$$−$$id))$$    $$=0$$⇒                             bc−$$ad=0$$⇒ad−bc    $$=0$$

If the points represented by complex numbers $z_{1} = a + i b, z_{2} = c + i d$ and $z_{1} - z_{2}$ are collinear, where $i = \sqrt{- 1}$ then

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If the points represented by complex numbers z1=a+ib,z2=c+id and z1−z2 are collinear, where i=−1 then

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If the points represented by complex numbers $z_{1} = a + i b, z_{2} = c + i d$ and $z_{1} - z_{2}$ are collinear, where $i = \sqrt{- 1}$ then