Advertisements
Advertisements
प्रश्न
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Advertisements
उत्तर
`((3 + isqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
= `((3)^2 - (isqrt5)^2)/(sqrt3 + sqrt2i - sqrt3 + sqrt2i` `[(a+b) (a +b) = a^2 - b^2]`
= `(9 - 5i)^2/(2 sqrt2i)`
= `(9 - 5 (-1))/(2 sqrt2i)` `[i^2 = -1]`
= `(9 + 5)/(2 sqrt2i) xx i/i`
= `(14i)/((2sqrt2) (-1))`
= - `(7i)/sqrt2 xx sqrt2/sqrt2`
= `(-7 sqrt2i)/2`
APPEARS IN
संबंधित प्रश्न
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Find the value of: x3 – 5x2 + 4x + 8, if x = `10/(3 - "i")`.
Write the conjugates of the following complex number:
5i
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
If a = `(-1 + sqrt(3)"i")/2`, b = `(-1 - sqrt(3)"i")/2` then show that a2 = b and b2 = a
If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)
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(1 + 3i) + y(2 − i) − 5 + i3 = 0, find x + y
Answer the following:
Simplify the following and express in the form a + ib:
(2i3)2
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:
`(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")`
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
Evaluate: (1 + i)6 + (1 – i)3
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
State true or false for the following:
The complex number cosθ + isinθ can be zero for some θ.
State true or false for the following:
The argument of the complex number z = `(1 + i sqrt(3))(1 + i)(cos theta + i sin theta)` is `(7pi)/12 + theta`.
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.
What is the principal value of amplitude of 1 – i?
Number of solutions of the equation z2 + |z|2 = 0 is ______.
Solve the equation |z| = z + 1 + 2i.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
If `((1 + i)/(1 - i))^x` = 1, then ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
If z1, z2, z3 are complex numbers such that |z1| = |z2| = |z3| = `|1/z_1 + 1/z_2 + 1/z_3|` = 1, then |z1 + z2 + z3| is ______.
Let z be a complex number such that `|(z - i)/(z + 2i)|` = 1 and |z| = `5/2`. Then the value of |z + 3i| is ______.
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)`
Evaluate the following:
i35
