There exists a complex z satisfying the following iz 1 i z

There exists a complex z satisfying the following: iz + 1 = i z - 2 = -1 + i

Solution

iz+ 1 =i

multiply with -i on both sides

=>-i(iz+ 1 =i)

=>-i²z -i =- i²

=>-(-1)z -i =-(-1)

=> z -i =1

=> z =1 +i

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from second equation

z -2 =-1 +i

z=2-1 +i

z =1 +i

true

, there exists complex number z i.e, 1+i satisfying both equations