Advertisements
Advertisements
प्रश्न
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
उत्तर
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
= `((sqrt(5) + sqrt(3)"i")(sqrt(5) + sqrt(3)"i"))/((sqrt(5) - sqrt(3)"i")(sqrt(5) + sqrt(3)"i")`
= `(5 + 2sqrt(15)"i" + 3"i"^2)/(5 - 3"i"^2)`
= `(5 + 2sqrt(15)"i" + 3(-1))/(5 - 3(-1)` ...[∵ i2 = – 1]
= `(2 + 2sqrt(15)"i")/8`
= `(1 + sqrt(15)"i")/4`
= `1/4 + (sqrt(15)"i")/4`.
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
Simplify the following and express in the form a + ib:
(2i3)2
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)
Answer the following:
Simplify the following and express in the form a + ib:
`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`
Answer the following:
Evaluate: (1 − i + i2)−15
Answer the following:
Find the real numbers x and y such that `x/(1 + 2"i") + y/(3 + 2"i") = (5 + 6"i")/(-1 + 8"i")`
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 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.
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
Which of the following is correct for any two complex numbers z1 and z2?
If a + ib = c + id, then ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.
Show that `(-1 + sqrt3 i)^3` is a real number.
