COMEDK2016MathematicsComplex Number
The complex number (- 3 +3 i)(1-i) (3+ 3 i)(i)( 3 + 3 i) , when represented in the Argand diagram lies
Options
- Aon the X -axis (Real axis)
- Bon the Y_ -axis (Imaginary axis)
- Cin the first quadrant
- Din the second quadrant
Correct answer
B. on the Y_ -axis (Imaginary axis)
Step-by-step solution
Let aligned &= (- 3 +3 i)(1-i) (3+ 3 i)(i)( 3 + 3 i) &= 3 (-1+ 3 i)(1-i) ( 3 )²( 3 +i)(1+i)(i) &= (-1+ 3 i)(1-i) 3 ( 3 i+i² )(1+i) = (-1+ 3 i )(1-i) 3 (-1+ 3 i )(1+i) &= 1-i ( 3 ) 1+i (1-i) (1-i) = (1-i)² ( 3 )(1+1) &= 1+i²-2 i 2 3 = -2 i 2 3 =- i 3 &= Purely imaginary aligned