If z(2-i)=(3+i) , then z³⁸=,( where z=x+ iy )

Step-by-step solution

We have (x+i y)(2-i)=3+i 2 x+(2 y-x) i+y=3+i Solving eq. (1) and (2), we get aligned & x=1, y=1 z=1+i= 2 ( 1 2 + i 1 2 ) & z = 2 ( 4 + i 4 ) & z ³⁸=( 2 )³⁸ ( 38 4 + i 38 4 ) & =(2)¹⁹ [ (9 + 2 )+ i (9 + 2 ) ] & =(2)¹⁹ (- 2 - i 2 )=2¹⁹(0-i) & =- (2¹⁹ ) i aligned