The number of solutions of the equation z ²+ z =0 , where z C , are

Step-by-step solution

Let z=x+i y aligned & z²=x²-y²+2 i x y & z²+ z =0 & x²-y²+2 i x y+x-i y=0 & (x²+x-y² )+i(2 x y-y)=0 aligned Equating the real and imaginary parts, we get x²+x-y²=0 and 2 x y-y=0 (ii) By Eq. (ii), we get y(2 x-1)=0 y =0 or x = 1 2 On solving these two with first equation, we get four solutions (0,0),(-1,0) and ( 1 2 , 3 2 ) .