Advertisements
Advertisements
Question
If 2 = x + iy is a complex number such that `|(z - 4"i")/(z + 4"i")|` = 1 show that the locus of z is real axis
Advertisements
Solution
`|(z - 4"i")/(z + 4"i")|` = 1
⇒ |z – 4i| = |z + 4i|
Let z = x + iy
⇒ |x + iy – 4i| = |x + iy + 4i|
⇒ |x + i(y – 4)| = |x +(y + 4)|
⇒ `sqrt(x^2 + (y - 4)^2`
= `sqrt(x^2 + (y + 4)^2`
Squaring on both sides, we get
x2 + y2 – 8y + 16 = x2 + y2 + 16 + 8y
⇒ – 16y = 0
⇒ y = 0 in two equation of real axis.
APPEARS IN
RELATED QUESTIONS
If z = x + iy is a complex number such that Im `((2z + 1)/("i"z + 1))` = 0, show that the locus of z is 2x2 + 2y2 + x – 2y = 0
Obtain the Cartesian form of the locus of z = x + iy in the following cases:
[Re(iz)]2 = 3
Obtain the Cartesian form of the locus of z = x + iy in the following cases:
Im[(1 – i)z + 1] = 0
Obtain the Cartesian form of the locus of z = x + iy in the following cases:
`bar(z) = z^-1`
Show that the following equations represent a circle, and, find its centre and radius.
|z – 2 – i| = 3
Show that the following equations represent a circle, and, find its centre and radius.
|2z + 2 – 4i| = 2
Show that the following equations represent a circle, and, find its centre and radius.
|3z – 6 + 12i| = 8
Obtain the Cartesian equation for the locus of z = x + iy in the following cases:
|z – 4| = 16
Obtain the Cartesian equation for the locus of z = x + iy in the following cases:
|z – 4|2 – |z – 1|2 = 16
Choose the correct alternative:
If `|"z" - 3/2|`, then the least value of |z| is
Choose the correct alternative:
If |z1| = 1,|z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is
Choose the correct alternative:
If z = x + iy is a complex number such that |z + 2| = |z – 2|, then the locus of z is
Choose the correct alternative:
The principal argument of the complex number `((1 + "i" sqrt(3))^2)/(4"i"(1 - "i" sqrt(3))` is
