Advertisements
Advertisements
प्रश्न
Multiplicative inverse of 1 + i is ______.
उत्तर
Multiplicative inverse of 1 + i is `underlinebb(1/2 (1 - i))`.
Explanation:
Multiplicative inverse of 1 + i = `1/(1 + i)`
= `(1 xx (1 - i))/((1 + i)(1 - i))`
= `(1 - i)/(1 - i^2)`
= `(1 - i)/(1 + 1)`
= `1/2(1 - i)`
APPEARS IN
संबंधित प्रश्न
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.
Find the value of i + i2 + i3 + i4
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
Simplify the following and express in the form a + ib:
`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Evaluate: `("i"^37 + 1/"i"^67)`
If (a + ib) = `(1 + "i")/(1 - "i")`, then prove that (a2 + b2) = 1
Answer the following:
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Answer the following:
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "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")`
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 z = `((-1 + sqrt(-3))/2)^3` is a rational number
If `(x + iy)^(1/3)` = a + ib, where x, y, a, b ∈ R, show that `x/a - y/b` = –2(a2 + b2)
The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real is ______.
The value of `(- sqrt(-1))^(4"n" - 3)`, where n ∈ N, is ______.
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
If (1 + i)z = `(1 - i)barz`, then show that z = `-ibarz`.
If `((1 + i)/(1 - i))^x` = 1, then ______.
If a + ib = c + id, then ______.
The complex number z which satisfies the condition `|(i + z)/(i - z)|` = 1 lies on ______.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
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.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18`
Evaluate the following:
i35
