Advertisements
Advertisements
प्रश्न
Find a and b if `1/("a" + "ib")` = 3 – 2i
Advertisements
उत्तर
`1/("a" + "ib")` = 3 – 2i
∴ a + ib = `1/(3 - 2"i")`
∴ a + ib = `1/(3 - 2"i") xx (3 + 2"i")/(3 + 2"i")`
∴ a + ib = `(3 + 2"i")/(9 - 4"i"^2)`
∴ a + ib = `(3 + 2"i")/(9 + 4)` ...[∵ i2 = – 1]
∴ a + ib = `(3 + 2"i")/13 = 3/13 + 2/13 "i"`
Equating the real and imaginary parts separately, we get,
a = `3/13`, b = `2/13`
APPEARS IN
संबंधित प्रश्न
Express the given complex number in the form a + ib: `(5i) (- 3/5 i)`
Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`
Express the given complex number in the form a + ib: (1 – i)4
Express the following complex number in the standard form a + i b:
\[(1 + i)(1 + 2i)\]
Express the following complex number in the standard form a + i b:
\[\frac{3 - 4i}{(4 - 2i)(1 + i)}\]
Find the real value of x and y, if
\[(x + iy)(2 - 3i) = 4 + i\]
If \[z_1 = 2 - i, z_2 = 1 + i,\text { find } \left| \frac{z_1 + z_2 + 1}{z_1 - z_2 + i} \right|\]
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Re \[\left( \frac{z_1 z_2}{z_1} \right)\]
If \[\frac{\left( 1 + i \right)^2}{2 - i} = x + iy\] find x + y.
Evaluate the following:
\[2 x^3 + 2 x^2 - 7x + 72, \text { when } x = \frac{3 - 5i}{2}\]
For a positive integer n, find the value of \[(1 - i )^n \left( 1 - \frac{1}{i} \right)^n\].
If z1 is a complex number other than −1 such that \[\left| z_1 \right| = 1\] and \[z_2 = \frac{z_1 - 1}{z_1 + 1}\] then show that the real parts of z2 is zero.
Write (i25)3 in polar form.
Express the following complex in the form r(cos θ + i sin θ):
1 − sin α + i cos α
Write the argument of −i.
Find the principal argument of \[\left( 1 + i\sqrt{3} \right)^2\] .
If \[\left| z \right| = 2 \text { and } \arg\left( z \right) = \frac{\pi}{4}\],find z.
Write the argument of \[\left( 1 + i\sqrt{3} \right)\left( 1 + i \right)\left( \cos\theta + i\sin\theta \right)\].
Disclaimer: There is a misprinting in the question. It should be \[\left( 1 + i\sqrt{3} \right)\] instead of \[\left( 1 + \sqrt{3} \right)\].
The value of \[(1 + i)(1 + i^2 )(1 + i^3 )(1 + i^4 )\] is.
The polar form of (i25)3 is
If \[z = \frac{- 2}{1 + i\sqrt{3}}\],then the value of arg (z) is
If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals
\[\text { If } z = \frac{1}{(1 - i)(2 + 3i)}, \text { than } \left| z \right| =\]
If θ is the amplitude of \[\frac{a + ib}{a - ib}\] , than tan θ =
If \[f\left( z \right) = \frac{7 - z}{1 - z^2}\] , where \[z = 1 + 2i\] then \[\left| f\left( z \right) \right|\] is
If z is a complex number, then
Which of the following is correct for any two complex numbers z1 and z2?
Simplify : `sqrt(-16) + 3sqrt(-25) + sqrt(-36) - sqrt(-625)`
Find a and b if a + 2b + 2ai = 4 + 6i
Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:
`((1 + "i")/(1 - "i"))^2`
Express the following in the form of a + ib, a, b ∈ R i = `sqrt(−1)`. State the values of a and b:
`(- sqrt(5) + 2sqrt(-4)) + (1 -sqrt(-9)) + (2 + 3"i")(2 - 3"i")`
Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:
(2 + 3i)(2 – 3i)
Show that `(-1 + sqrt(3)"i")^3` is a real number
Evaluate the following : i35
Evaluate the following : i403
If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.
If `((1 - i)/(1 + i))^100` = a + ib, then find (a, b).
State True or False for the following:
2 is not a complex number.
If w is a complex cube-root of unity, then prove the following
(w2 + w − 1)3 = −8
