If a complex number lies in the III quadrant. Find the quadrant in which its. conjugate lies.

Question

If a complex number lies in the III quadrant. Find the quadrant in which its. conjugate lies. (A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant

Tardigrade Admin · Accepted Answer

Let z =a+ ib then in III quadrant a < 0, b < 0 Its conjugate barz = a +ib = a -ib = a+ (-ib) = a + ik where k = -b ⇒ : : a < 0, k > 0 ⇒ : : barz lies in II quadrant,

Q. If a complex number lies in the III quadrant. Find the quadrant in which its. conjugate lies.

I quadrant

II quadrant

III quadrant

IV quadrant

Let $z = a + ib$ then in III quadrant $a < 0, b < 0$
Its conjugate $\overset{z}{ˉ} = a + ib = a - ib = a + (- ib)$
= $a + ik$ where $k = - b$
$\Rightarrow a < 0, k > 0$
$\Rightarrow \overset{z}{ˉ}$ lies in II quadrant,

Q. If a complex number lies in the III quadrant. Find the quadrant in which its. conjugate lies.

I quadrant

II quadrant

III quadrant

IV quadrant

Let z=a+ib then in III quadrant a<0,b<0 Its conjugate zˉ=a+ib=a−ib=a+(−ib) = a+ik where k=−b ⇒a<0,k>0 ⇒zˉ lies in II quadrant,

Let $z = a + ib$ then in III quadrant $a < 0, b < 0$
Its conjugate $\overset{z}{ˉ} = a + ib = a - ib = a + (- ib)$
= $a + ik$ where $k = - b$
$\Rightarrow a < 0, k > 0$
$\Rightarrow \overset{z}{ˉ}$ lies in II quadrant,