Advertisements
Advertisements
प्रश्न
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.
पर्याय
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
Let z = 2 + 3i be complex number represented by OP.
Then iz = –3 + 2i, represented by OQ.
Where if OP is rotated in the anticlockwise direction through a right angle, It coincides with OQ.
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Find the value of i + i2 + i3 + i4
Find the value of: x3 – x2 + x + 46, if x = 2 + 3i
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
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
Answer the following:
Simplify the following and express in the form a + ib:
(2 + 3i)(1 − 4i)
Answer the following:
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Answer the following:
Evaluate: i131 + i49
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
Answer the following:
Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
If z ≠ 1 and `"z"^2/("z - 1")` is real, then the point represented by the complex number z lies ______.
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
The value of (2 + i)3 × (2 – i)3 is ______.
If `(x + iy)^(1/3)` = a + ib, where x, y, a, b ∈ R, show that `x/a - y/b` = –2(a2 + b2)
What is the value of `(i^(4n + 1) -i^(4n - 1))/2`?
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
Find the complex number satisfying the equation `z + sqrt(2) |(z + 1)| + i` = 0.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
Multiplicative inverse of 1 + i is ______.
State True or False for the following:
Multiplication of a non-zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.
If a + ib = c + id, then ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` 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)`
Find the value of `sqrt(-3) xx sqrt(-6)`
Show that `(-1 + sqrt3i)^3` is a real number.
