Mirror image of point (x, y) on imaginary axis is (-x, y).
Since imaginary axis is acting as mirror y-coordinate remains same whereas x-coordinate gets inverted. So, (-x, y) is mirror image of (x, y) on imaginary axis.

On multiplying one (1+0i) to a complex number, we get same complex number so 1+0i is multiplicative identity element for complex number z i.e. z*1=z.

We know, i = \(\sqrt{-1}\)
=> i² = -1 => i⁴ = 1.
So, i⁷ = i⁴.i³ = 1*i²*i = (-1)*i = -i.

We know, i = \(\sqrt{-1}\)
=> i² = -1.

We have, (2x² – 2x ? 3) / (x² + x + 1) ≤ a ᵾ x € R
=> 2x² – 2x ? 3 ? a(x² + x + 1) ᵾ x € R
=> (2 ? a)x² – (2 ? a)x ? (3 ? a) ᵾ x € R
2 ? a < 0 and (2 ? a)x² ? 4(2 ? a)(3 ? a) ≤ 0 ᵾ x € R
So, a > 2 and a ≤ 2 or a ≥ 10/3
=> a ≥ 10/3
Therefore, a € [10/3, ∞)

x²+1 = 0
=>x² = -1 => x = ±\(\sqrt{-1}\) = ±i.

Comparing coefficients of above equation we get,
1/1 = b/3 = c/3
This means b = 3 and c = 3
Therefore, b + c = 6.

r=\(\sqrt{x^2+y^2}=\sqrt{(-1)^2+1^2}=\sqrt{1+1}=\sqrt{2}\).
r cos &ta; = -1 and r sin &ta; = 1 So, &ta; is in 2^nd quadrant since sin is positive and cos is negative.
tan &ta; = -1 => tan &ta; = -tan π/4
=> tan &ta; = tan (π-π/4) = tan 3π/4
=> &ta;=3π/4.

If two complex numbers are equal, n corresponding parts are equal i.e. real parts of both are equal and imaginary parts of both are equal.
x+3 = 5 and y-2 = 2
x = 5-3 and y = 2+2
x=2 and y=4.

Conjugate complex numbers means ir real part is same and imaginary part is inverted i.e. same x part and opposite imaginary part. So, y are mirror image on real axis i.e. x-axis.