Advertisements
Advertisements
प्रश्न
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
उत्तर
(x + iy) (5 + 6i) = 2 + 3i
∴ x + iy = `(2 + 3"i")/(5 + 6"i")`
∴ x + iy = `((2 + 3"i")(5 - 6"i"))/((5 + 6"i")(5 - 6"i"))`
= `(10 - 12"i" + 15"i" - 18"i"^2)/(25 - 36"i"^2)`
= `(10 + 3"i" - 18(-1))/(25 - 36(-1))`
∴ x + iy = `(28 + 3"i")/61`
= `28/61 + 3/61"i"`
Equating real and imaginary parts, we get
x = `28/61` and y = `3/61`
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number.
`sqrt5 + 3i`
Express the following expression in the form of a + ib.
`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`
Show that 1 + i10 + i20 + i30 is a real number.
Find the value of i49 + i68 + i89 + i110
Is (1 + i14 + i18 + i22) a real number? Justify your answer
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Find the value of x and y which satisfy the following equation (x, y∈R).
`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i
Find the value of x and y which satisfy the following equation (x, y ∈ R).
`((x + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`
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:
(2 + 3i)(1 − 4i)
Answer the following:
Simplify the following and express in the form a + ib:
(1 + 3i)2(3 + 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 ______.
The real value of ‘a’ for which 3i3 – 2ai2 + (1 – a)i + 5 is real is ______.
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 locus of z, if amplitude of z – 2 – 3i is `pi/4`?
1 + i2 + i4 + i6 + ... + i2n is ______.
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
The area of the triangle on the complex plane formed by the complex numbers z, –iz and z + iz is ______.
For a positive integer n, find the value of `(1 - i)^n (1 - 1/i)^"n"`
If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.
For any two complex numbers z1, z2 and any real numbers a, b, |az1 – bz2|2 + |bz1 + az2|2 = ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
State True or False for the following:
The inequality |z – 4| < |z – 2| represents the region given by x > 3.
The value of `(z + 3)(barz + 3)` is equivalent to ______.
If `((1 + i)/(1 - i))^x` = 1, then ______.
A real value of x satisfies the equation `((3 - 4ix)/(3 + 4ix))` = α − iβ (α, β ∈ R) if α2 + β2 = ______.
`((1 + cosθ + isinθ)/(1 + cosθ - isinθ))^n` = ______.
If α, β, γ and a, b, c are complex numbers such that `α/a + β/b + γ/c` = 1 + i and `a/α + b/β + c/γ` = 0, then the value of `α^2/a^2 + β^2/b^2 + γ^2/c^2` is equal to ______.
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)`
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)`
