KCET2011MathematicsComplex Number
In Argand's plane, the point corresponding to (1-i 3 )(1+i) ( 3 +i) lies in
Options
- Aquadrant I
- Bquadrant II
- Cquadrant III
- Dquadrant IV
Correct answer
D. quadrant IV
Step-by-step solution
Given, aligned & (1-i 3 )(1+i) ( 3 +i) = (1-i 3 +i+ 3 )( 3 -i) (3+1) &= 1 4 (1+ 3 )+i(1- 3 ) ( 3 -i) &= 1 4 3 (1+ 3 )+i(1- 3 ) 3 & .= 1 4 3 +3+1- 3 )+( 3 -3-1- 3 ) i &= 1 4 4-4 i =1-i aligned The point (1-i) in Arg and plane is (1,-1) which lies in IVth quadrant.