Q. 25 I4.6( 5 Votes )

# Fill in the blanks of the following

If then the locus of z is ………….

Answer :

**Explanation:**

Given

⇒ 6 |x – 2 + iy| = π |x + 2 + iy|

Squaring on both sides,

⇒ 36 |x – 2 + iy|^{2} = π^{2} |x + 2 + iy|^{2}

⇒ 36 [x^{2} – 4x + 4 + y^{2}] = π^{2} [x^{2} – 4x + 4 + y^{2}]

⇒ (36 – π^{2}) x^{2} + (36 – π^{2}) y^{2} – (144 + 4π^{2}) x + 144 – 4π^{2} = 0

Which is a circle.

Rate this question :

If z and w are two complex numbers such that |zw| = 1 and arg (z) – arg (w) = π/2, then show that

Mathematics - ExemplarState True of False for the following:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.

Mathematics - ExemplarState True of False for the following:

If z is a complex number such that z ≠ 0 and Re (z) = 0, then Im (z^{2}) = 0.

State True of False for the following:

The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).

Mathematics - ExemplarSolve for x: (1 – i) x + (1 + i) y = 1 – 3i.

RS Aggarwal - MathematicsFind the real value of a for which 3i^{3} – 3ai^{2} + (1 – a) i + 5 is real.

If n ∈ N, then find the value of i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}.

Write the least positive integral value of n for which is real.

RD Sharma - MathematicsIf find the value of x^{2} + y^{2}.

If n is any positive integer, write the value of

RD Sharma - Mathematics