Advertisements
Advertisements
प्रश्न
What is the principal value of amplitude of 1 – i?
Advertisements
उत्तर
Let θ be the principal value of amplitude of 1 – i.
Since tanθ = –1
⇒ tanθ = `tan(- pi/4)`
⇒ θ = `- pi/4`
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.
Find the number of non-zero integral solutions of the equation `|1-i|^x = 2^x`.
Show that 1 + i10 + i20 + i30 is a real number.
Find the value of: 2x3 – 11x2 + 44x + 27, if x = `25/(3 - 4"i")`
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Find the value of: x3 – 3x2 + 19x – 20, if x = 1 – 4i
Write the conjugates of the following complex number:
3 – i
Write the conjugates of the following complex number:
`-sqrt(-5)`
Write the conjugates of the following complex number:
cosθ + i sinθ
Find the value of 1 + i2 + i4 + i6 + i8 + ... + i20
Show that 1 + i10 + i100 − i1000 = 0
Select the correct answer from the given alternatives:
`sqrt(-3) sqrt(-6)` is equal to
Answer the following:
Evaluate: (1 − i + i2)−15
Answer the following:
Find the value of x3 + 2x2 − 3x + 21, if x = 1 + 2i
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:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
Answer the following:
Simplify `[1/(1 - 2"i") + 3/(1 + "i")] [(3 + 4"i")/(2 - 4"i")]`
The value of (2 + i)3 × (2 – i)3 is ______.
State true or false for the following:
The complex number cosθ + isinθ can be zero for some θ.
State true or false for the following:
If n is a positive integer, then the value of in + (i)n+1 + (i)n+2 + (i)n+3 is 0.
What is the smallest positive integer n, for which (1 + i)2n = (1 – i)2n?
1 + i2 + i4 + i6 + ... + i2n is ______.
If |z + 1| = z + 2(1 + i), then find z.
The value of `sqrt(-25) xx sqrt(-9)` 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.
Find `|(1 + i) ((2 + i))/((3 + i))|`.
Let x, y ∈ R, then x + iy is a non-real complex number if ______.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
If `(x + iy)^(1/5)` = a + ib, and u = `x/a - y/b`, then ______.
A complex number z is moving on `arg((z - 1)/(z + 1)) = π/2`. If the probability that `arg((z^3 -1)/(z^3 + 1)) = π/2` is `m/n`, where m, n ∈ prime, then (m + n) is equal to ______.
Let z be a complex number such that `|(z - i)/(z + 2i)|` = 1 and |z| = `5/2`. Then the value of |z + 3i| 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 ______.
Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals 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.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Evaluate the following:
i35
Show that `(-1 + sqrt3i)^3` is a real number.
