Advertisements
Advertisements
प्रश्न
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Advertisements
उत्तर
`(4 + 3"i")/(1 - "i") = ((4 + 3"i")(1 + "i"))/((1 - "i")(1 + "i")`
= `(4 + 4"i" + 3"i" + 3"i"^2)/(1 - "i"^2)`
= `(4 + 7"i" + 3(-1))/(1 - (-1)` ...[∵ i2 = – 1]
= `(1 + 7"i")/2`
= `1/2+7/2"i"`.
APPEARS IN
संबंधित प्रश्न
If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`
Show that 1 + i10 + i20 + i30 is a real number.
Write the conjugates of the following complex number:
3 + i
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 + "i"y))/(2 + 3"i") + (2 + "i")/(2 - 3"i") = 9/13(1 + "i")`
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:
`(4 + 3"i")/(1 - "i")`
Answer the following:
Solve the following equations for x, y ∈ R:
(x + iy) (5 + 6i) = 2 + 3i
Answer the following:
Evaluate: (1 − i + i2)−15
Answer the following:
Show that `(1 - 2"i")/(3 - 4"i") + (1 + 2"i")/(3 + 4"i")` is real
Answer the following:
Simplify: `("i"^65 + 1/"i"^145)`
Evaluate: (1 + i)6 + (1 – i)3
Locate the points for which 3 < |z| < 4.
What is the reciprocal of `3 + sqrt(7)i`.
If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).
The value of `(z + 3)(barz + 3)` is equivalent to ______.
Which of the following is correct for any two complex numbers z1 and z2?
