Advertisements
Advertisements
प्रश्न
Simplify the following and express in the form a + ib:
`5/2"i"(- 4 - 3 "i")`
Advertisements
उत्तर
`5/2"i"(- 4 - 3 "i")`
= `5/2(- 4"i" - 3 "i"^2)`
= `5/2[-4"i" - 3(-1)]` ...[∵ i2 = – 1]
= `5/2(3 - 4"i")`
= `15/2 - 10"i"`
APPEARS IN
संबंधित प्रश्न
Find the value of i49 + i68 + i89 + i110
Show that 1 + i10 + i100 − i1000 = 0
Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`
If x + iy = `sqrt(("a" + "ib")/("c" + "id")`, prove that (x2 + y2)2 = `("a"^2 + "b"^2)/("c"^2 + "d"^2)`
Show that `((sqrt(7) + "i"sqrt(3))/(sqrt(7) - "i"sqrt(3)) + (sqrt(7) - "i"sqrt(3))/(sqrt(7) + "i"sqrt(3)))` is real
Find the value of x and y which satisfy the following equation (x, y∈R).
If x(1 + 3i) + y(2 − i) − 5 + i3 = 0, find x + y
Select the correct answer from the given alternatives:
The value of is `("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)` is equal to:
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:
Find the value of x4 + 9x3 + 35x2 − x + 164, if x = −5 + 4i
Answer the following:
Simplify: `("i"^238 + "i"^236 + "i"^234 + "i"^232 + "i"^230)/("i"^228 + "i"^226 + "i"^224 + "i"^222 + "i"^220)`
Evaluate: (1 + i)6 + (1 – i)3
If (2 + i) (2 + 2i) (2 + 3i) ... (2 + ni) = x + iy, then 5.8.13 ... (4 + n2) = ______.
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 ______.
If `(z - 1)/(z + 1)` is purely imaginary number (z ≠ – 1), then find the value of |z|.
Let |z| = |z – 3| = |z – 4i|, then the value |2z| is ______.
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 ______.
If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.
Evaluate the following:
i35
