Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
उत्तर
This statement is False.
Explanation:
Let z = x + yi
z.i = (x + yi)i = xi – y
Which rotates at angle of 180°.
APPEARS IN
संबंधित प्रश्न
Show that 1 + i10 + i20 + i30 is a real number.
Simplify the following and express in the form a + ib:
(2i3)2
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:
3 – i
Write the conjugates of the following complex number:
`sqrt(5) - "i"`
Write the conjugates of the following complex number:
cosθ + i sinθ
If `("a" + 3"i")/(2+ "ib")` = 1 − i, show that (5a − 7b) = 0
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real
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:
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:
2x + i9y (2 + i) = xi7 + 10i16
Answer the following:
Evaluate: i131 + i49
State true or false for the following:
The complex number cosθ + isinθ can be zero for some θ.
1 + i2 + i4 + i6 + ... + i2n is ______.
For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
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 ______.
If α and β are the roots of the equation x2 + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.
Find the value of `(i^592+i^590+i^588+i^586+i^584)/(i^582+i^580+i^578+i^576+i^574)`
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 + sqrt3 i)^3` is a real number.
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
Show that `(-1 + sqrt3i)^3` is a real number.
