Advertisements
Advertisements
Question
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
Options
|z|2
`|barz|^2`
`|z|^2/2`
None of these
Solution
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
RELATED QUESTIONS
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
Find the value of i + i2 + i3 + i4
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
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)`
Write the conjugates of the following complex number:
`-sqrt(-5)`
Write the conjugates of the following complex number:
5i
Show that 1 + i10 + i100 − i1000 = 0
Evaluate : `("i"^37 + 1/"i"^67)`
Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`
Answer the following:
Simplify the following and express in the form a + ib:
(1 + 3i)2(3 + i)
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
Answer the following:
Evaluate: i131 + i49
If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.
The value of (2 + i)3 × (2 – i)3 is ______.
State true or false for the following:
Multiplication of a non-zero complex number by i rotates it through a right angle in the anti-clockwise direction.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
Multiplicative inverse of 1 + i is ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
State True or 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).
If `((1 + i)/(1 - i))^x` = 1, then ______.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
If z is a complex number, then ______.
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18`
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)`
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Show that `(-1 + sqrt3i)^3` is a real number.
