Advertisements
Advertisements
प्रश्न
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Advertisements
उत्तर
(2 + 3i)(1 – 4i)
= 2 – 8i + 3i – 12i2
= 2 – 5i – 12(– 1) ...[∵ i2 = – 1]
= 14 – 5i
APPEARS IN
संबंधित प्रश्न
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 + 2/i)(3 + 4/i)(5 + i)^-1`
Show that 1 + i10 + i100 − i1000 = 0
Find the value of x and y which satisfy the following equation (x, y∈R).
If x + 2i + 15i6y = 7x + i3 (y + 4), find x + y
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:
`(1 + 2/"i")(3 + 4/"i")(5 + "i")^-1`
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")`
The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______
What is the locus of z, if amplitude of z – 2 – 3i is `pi/4`?
Evaluate `sum_(n = 1)^13 (i^n + i^(n + 1))`, where n ∈ N.
If |z1| = 1(z1 ≠ –1) and z2 = `(z_1 - 1)/(z_1 + 1)`, then show that the real part of z2 is zero.
The sum of the series i + i2 + i3 + ... upto 1000 terms is ______.
Which of the following is correct for any two complex numbers z1 and z2?
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
If a complex number z satisfies the equation `z + sqrt(2)|z + 1| + i` = 0, then |z| is equal to ______.
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 ______.
The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.
Show that `(-1 + sqrt3 i)^3` is a real number.
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)`
