Q22 of 66 Page 91

Find the complex number satisfying the equation

Given equation z + √2 |(z + 1)| + i = 0 … (1)


Putting z = x + iy, we get


⇒ x + iy + √2 |x + iy + 1| + i = 0




Comparing real and imaginary parts to zero, we get


… (2)


And y + 1 = 0


⇒ y = -1


Putting y = -1 into (2), we get




⇒ 2x2 + 4x + 4 = x2


⇒ x2 + 4x + 4 = 0


⇒ (x + 2)2 = 0


⇒ x = -2


∴ z = x + iy


= -2 – i


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