Complex Numbers 2 Question 44

45. Find the real values of x and y for which the following equation is satisfied

(1+i)x−2i3+i+(2−3i)y+i3−i=i. 

(1980,2M)

Show Answer

Solution:

  1. (1+i)x−2i3+i+(2−3i)y+i3−i=i

⇒(1+i)(3−i)x−2i(3−i)+(3+i)(2−3i)y

+i(3+i)=10i

⇒4x+2ix−6i−2+9y−7iy+3i−1=10i

⇒4x+9y−3=0 and 2x−7y−3=10

⇒x=3 and y=−1

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