Advertisements
Advertisements
प्रश्न
Answer the following:
Evaluate: i131 + i49
Advertisements
उत्तर
i131 + i49
= i130.i + i48.i
= (i2)65.i + (i2)24.i
= (– 1)65.i + (– 1)24.i
= – i + i
= 0.
APPEARS IN
संबंधित प्रश्न
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
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:
`5/2"i"(- 4 - 3 "i")`
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Show that 1 + i10 + i100 − i1000 = 0
Is (1 + i14 + i18 + i22) a real number? Justify your answer
If x + iy = (a + ib)3, show that `x/"a" + y/"b"` = 4(a2 − b2)
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 :
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
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:
`(4 + 3"i")/(1 - "i")`
Solve the following equation for x, y ∈ R:
2x + i9y (2 + i) = xi7 + 10i16
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")`
Show that `(1/sqrt(2) + "i"/sqrt(2))^10 + (1/sqrt(2) - "i"/sqrt(2))^10` = 0
Answer the following:
show that `((1 + "i")/sqrt(2))^8 + ((1 - "i")/sqrt(2))^8` = 2
The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
What is the reciprocal of `3 + sqrt(7)i`.
What is the principal value of amplitude of 1 – i?
1 + i2 + i4 + i6 + ... + i2n is ______.
Number of solutions of the equation z2 + |z|2 = 0 is ______.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ______.
The number `(1 - i)^3/(1 - i^2)` is equal to ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
If `((1 + i)/(1 - i))^x` = 1, then ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
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)`
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)`
i2 + i3 + ... + i4000 =
