Advertisements
Advertisements
प्रश्न
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
विकल्प
|z|2
`|barz|^2`
`|z|^2/2`
None of these
Advertisements
उत्तर
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is `underlinebb(|z|^2/2)`.
Explanation:
Let z = x + iy.
Then –iz = y – ix.
Therefore, z + iz = (x – y) + i(x + y)
Required area of the triangle = `1/2(x^2 + y^2) = |z|^2/2`.
APPEARS IN
संबंधित प्रश्न
Find the value of i49 + i68 + i89 + i110
Find the value of i + i2 + i3 + i4
Is (1 + i14 + i18 + i22) a real number? Justify your answer
If a = `(-1 + sqrt(3)"i")/2`, b = `(-1 - sqrt(3)"i")/2` then show that a2 = b and b2 = a
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+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i
Find the value of x and y which satisfy the following equation (x, y∈R).
If x(1 + 3i) + y(2 − i) − 5 + i3 = 0, find x + y
Select the correct answer from the given alternatives:
If n is an odd positive integer then the value of 1 + (i)2n + (i)4n + (i)6n is :
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
Answer the following:
Simplify the following and express in the form a + ib:
(1 + 3i)2(3 + i)
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Answer the following:
Evaluate: i131 + i49
Answer the following:
Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is
If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
State true or false for the following:
The points representing the complex number z for which |z + 1| < |z − 1| lies in the interior of a circle.
State true or false for the following:
If three complex numbers z1, z2 and z3 are in A.P., then they lie on a circle in the complex plane.
State true or false for the following:
If n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.
If `(1 + i)^2/(2 - i)` = x + iy, then find the value of x + y.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
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 ______.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
Which of the following is correct for any two complex numbers z1 and z2?
If z is a complex number, then ______.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
If α, β, γ and a, b, c are complex numbers such that `α/a + β/b + γ/c` = 1 + i and `a/α + b/β + c/γ` = 0, then the value of `α^2/a^2 + β^2/b^2 + γ^2/c^2` is equal to ______.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Evaluate the following:
i35
