Advertisements
Advertisements
Question
The equation |z + 1 – i| = |z – 1 + i| represents a ______.
Options
Straight line
Circle
Parabola
Hyperbola
Advertisements
Solution
The equation |z + 1 – i| = |z – 1 + i| represents a straight line.
Explanation:
|z + 1 – i| = |z – 1 + i|
⇒ |z – (–1 + i)| = |z – (1 – i)|
⇒ PA = PB Where A denotes the point (–1, 1), B denotes the point (1, –1) and P denotes the point (x, y).
⇒ z lies on the perpendicular bisector of the line joining A and B and perpendicular bisector is a straight line.
APPEARS IN
RELATED QUESTIONS
Find the multiplicative inverse of the complex number:
4 – 3i
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Simplify the following and express in the form a + ib:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Write the conjugates of the following complex number:
`-sqrt(-5)`
Write the conjugates of the following complex number:
cosθ + i sinθ
Is (1 + i14 + i18 + i22) a real number? Justify your answer
If (x + iy)3 = y + vi then show that `(y/x + "v"/y)` = 4(x2 – y2)
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Find the value of x and y which satisfy the following equation (x, y ∈ R).
`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`
Find the value of x and y which satisfy the following equation (x, y∈R).
If x + 2i + 15i6y = 7x + i3 (y + 4), find x + y
Answer the following:
Simplify the following and express in the form a + ib:
(1 + 3i)2(3 + i)
Answer the following:
Simplify the following and express in the form a + ib:
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Answer the following:
Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i
Answer the following:
Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number
If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.
The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real is ______.
What is the reciprocal of `3 + sqrt(7)i`.
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.
`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.
If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.
If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.
Simplify the following and express in the form a + ib.
`(3i^5 + 2i^7 + i^9) / (i^6 + 2i^8 + 3i^18)`
i2 + i3 + ... + i4000 =
If z = 2 + i, then (z − 1) `(barz − 5) + (barz − 1)` (z − 5) is equal to ______.
