Advertisements
Advertisements
प्रश्न
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ______ and ______.
उत्तर
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are 6 and 0.
Explanation:
Given that: |z + 4| ≤ 3
For the greatest value of |z + 1|.
= |z + 4 – 3| ≤ |z + 4| + |–3|
= |z + 4 – 3| ≤ 3 + 3 ......[∵ |z + 4| ≤ 3 and |–3| = 3]
= |z + 4 – 3| ≤ 6
Hence, the greatest value of |z + 1| is 6 and for the least value of |z + 1| = 0. .....[∵ The least value of the modulus of complex number is 0.]
APPEARS IN
संबंधित प्रश्न
If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.
Find the value of i + i2 + i3 + i4
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Find the value of : x3 + 2x2 – 3x + 21, if x = 1 + 2i
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Select the correct answer from the given alternatives:
If n is an odd positive integer then the value of 1 + (i)2n + (i)4n + (i)6n is :
Answer the following:
Simplify the following and express in the form a + ib:
`5/2"i"(-4 - 3"i")`
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:
`(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")`
Answer the following:
Evaluate: (1 − i + i2)−15
Answer the following:
Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real
Answer the following:
Simplify: `("i"^29 + "i"^39 + "i"^49)/("i"^30 + "i"^40 + "i"^50)`
The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______
If z1 = 2 – 4i and z2 = 1 + 2i, then `bar"z"_1 + bar"z"_2` = ______.
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
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.
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If the real part of `(barz + 2)/(barz - 1)` is 4, then show that the locus of the point representing z in the complex plane is a circle.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
Multiplicative inverse of 1 + i is ______.
Where does z lie, if `|(z - 5i)/(z + 5i)|` = 1.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
If `((1 + i)/(1 - i))^x` = 1, then ______.
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)`
