Advertisements
Advertisements
प्रश्न
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)
Advertisements
उत्तर
(2 + 3i)(2 – 3i) = 4 – 9i2
= 4 – 9(– 1) ...[∵ i2 = – 1]
= 4 + 9
= 13
∴ (2 + 3i)(2 – 3i) = 13 + 0i
∴ a = 13 and b = 0
APPEARS IN
संबंधित प्रश्न
Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)
Evaluate the following:
(ii) i528
Evaluate the following:
\[i^{37} + \frac{1}{i^{67}}\].
Evaluate the following:
\[\left( i^{41} + \frac{1}{i^{257}} \right)^9\]
Evaluate the following:
\[i^{49} + i^{68} + i^{89} + i^{110}\]
Find the value of the following expression:
1+ i2 + i4 + i6 + i8 + ... + i20
Express the following complex number in the standard form a + i b:
\[\frac{1}{(2 + i )^2}\]
Express the following complex number in the standard form a + i b:
\[\frac{2 + 3i}{4 + 5i}\]
Find the real value of x and y, if
\[(1 + i)(x + iy) = 2 - 5i\]
Find the smallest positive integer value of m for which \[\frac{(1 + i )^n}{(1 - i )^{n - 2}}\] is a real number.
Evaluate the following:
\[2 x^3 + 2 x^2 - 7x + 72, \text { when } x = \frac{3 - 5i}{2}\]
Solve the system of equations \[\text { Re }\left( z^2 \right) = 0, \left| z \right| = 2\].
Express the following complex in the form r(cos θ + i sin θ):
\[\frac{1 - i}{\cos\frac{\pi}{3} + i\sin\frac{\pi}{3}}\]
Write the value of \[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\] .
Write 1 − i in polar form.
Write the argument of −i.
If \[\frac{\left( a^2 + 1 \right)^2}{2a - i} = x + iy\] find the value of \[x^2 + y^2\].
Write the sum of the series \[i + i^2 + i^3 + . . . .\] upto 1000 terms.
Write the value of \[\arg\left( z \right) + \arg\left( \bar{z} \right)\].
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
The principal value of the amplitude of (1 + i) is
If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals
If \[z = \frac{1}{1 - cos\theta - i sin\theta}\] then Re (z) =
The argument of \[\frac{1 - i}{1 + i}\] is
The value of (i5 + i6 + i7 + i8 + i9) / (1 + i) is
A real value of x satisfies the equation \[\frac{3 - 4ix}{3 + 4ix} = a - ib (a, b \in \mathbb{R}), if a^2 + b^2 =\]
If z is a complex number, then
Express the following in the form of a + ib, a, b∈R i = `sqrt(−1)`. State the values of a and b:
`(3 + 2"i")/(2 - 5"i") + (3 -2"i")/(2 + 5"i")`
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:
`(4"i"^8 - 3"i"^9 + 3)/(3"i"^11 - 4"i"^10 - 2)`
Find the value of `(3 + 2/i) (i^6 - i^7) (1 + i^11)`.
Evaluate the following : i35
Evaluate the following : i30 + i40 + i50 + i60
Show that 1 + i10 + i20 + i30 is a real number
State True or False for the following:
2 is not a complex number.
Show that `(-1 + sqrt3 "i")^3` is a real number.
Show that `(-1+ sqrt(3)i)^3` is a real number.
Find the value of `(i^(592) + i^(590) + i^(588) + i^(586) + i^(584))/(i^(582) + i^(580) + i^(578) + i^(576) + i^(574))`
Show that `(-1+sqrt3i)^3` is a real number.
