Find the locus of the points representing the complex number z for which ${| z + 5 |}^{2} - {| z - 5 |}^{2} = 10$ .

x = \frac{5}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = \frac{3}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = \frac{1}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x = \frac{1}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $x = \frac{1}{2}$
${| z + 5 |}^{2} - {| z - 5 |}^{2} = 10$ .
or $(z + 5) (¯ ¯ ¯ z + 5) - (z - 5) (¯ ¯ ¯ z - 5) = 10$
or $5 (z + ¯ ¯ ¯ z) + 25 + 5 (z + ¯ ¯ ¯ z) - 25 = 10$
or $2 \times 2 x = 2$
or $x = \frac{1}{2}$
This is the equation of a straight line.
Ans: C

Suggest Corrections

Similar questions

z = x + i y

| z + 5 |^{2} - | z - 5 |^{2} = 10

z = x + i y

| z + 5 |^{2} - | z - 5 |^{2} = 10

\frac{x - 4}{2} = \frac{y - 5}{2} = \frac{z - 3}{1}

x + y + z = 2

z

{| z - 1 |}^{2} + {| z + 1 |}^{2} = 4

\frac{x - 2}{2} = \frac{y - 1}{5} = \frac{z + 3}{- 3}

\frac{x + 2}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4}

\frac{x}{2} = \frac{y}{2} = \frac{z}{1}

\frac{x - 5}{4} = \frac{y - 2}{1} = \frac{z - 3}{8}

Join BYJU'S Learning Program