Advertisements
Advertisements
Question
Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`
Advertisements
Solution
`(1/5 + i2/5) - (4 + i 5/2 )`
= `1/5 + 2/5 i-4 - 5/2i`
= `(-4+1/5) + (2/5-5/2)i`
= `((1 - 20)/5) + i ((4 - 25)/10)`
= `(-19)/5 + (4 - 25)/10 i`
= `(-19)/5 + (-21)/10i`
APPEARS IN
RELATED QUESTIONS
Express the given complex number in the form a + ib:
`[(1/3 + i 7/3) + (4 + i 1/3)] -(-4/3 + i)`
If a + ib = `(x + i)^2/(2x^2 + 1)` prove that a2 + b2 = `(x^2 + 1)^2/(2x + 1)^2`
Evaluate the following:
i457
Evaluate the following:
(ii) i528
Evaluate the following:
\[i^{30} + i^{40} + i^{60}\]
Evaluate the following:
\[i^{49} + i^{68} + i^{89} + i^{110}\]
Find the value of the following expression:
i + i2 + i3 + i4
Find the value of the following expression:
\[\frac{i^{592} + i^{590} + i^{588} + i^{586} + i^{584}}{i^{582} + i^{580} + i^{578} + i^{576} + i^{574}}\]
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:
\[\frac{(1 + i)(1 + \sqrt{3}i)}{1 - i}\] .
Express the following complex number in the standard form a + i b:
\[(1 + 2i )^{- 3}\]
Find the real value of x and y, if
\[(1 + i)(x + iy) = 2 - 5i\]
Find the real values of θ for which the complex number \[\frac{1 + i cos\theta}{1 - 2i cos\theta}\] is purely real.
Evaluate the following:
\[x^4 + 4 x^3 + 6 x^2 + 4x + 9, \text { when } x = - 1 + i\sqrt{2}\]
If \[\frac{z - 1}{z + 1}\] is purely imaginary number (\[z \neq - 1\]), find the value of \[\left| z \right|\].
Write (i25)3 in polar form.
Express the following complex in the form r(cos θ + i sin θ):
1 + i tan α
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 −1 + i \[\sqrt{3}\] in polar form .
If \[\frac{\left( a^2 + 1 \right)^2}{2a - i} = x + iy\] find the value of \[x^2 + y^2\].
Write the value of \[\arg\left( z \right) + \arg\left( \bar{z} \right)\].
For any two complex numbers z1 and z2 and any two real numbers a, b, find the value of \[\left| a z_1 - b z_2 \right|^2 + \left| a z_2 + b z_1 \right|^2\].
Find the real value of a for which \[3 i^3 - 2a i^2 + (1 - a)i + 5\] is real.
If i2 = −1, then the sum i + i2 + i3 +... upto 1000 terms is equal to
The least positive integer n such that \[\left( \frac{2i}{1 + i} \right)^n\] is a positive integer, is.
If \[z = \frac{1 + 2i}{1 - (1 - i )^2}\], then arg (z) equal
If \[x + iy = \frac{3 + 5i}{7 - 6i},\] then y =
If \[f\left( z \right) = \frac{7 - z}{1 - z^2}\] , where \[z = 1 + 2i\] then \[\left| f\left( z \right) \right|\] is
A real value of x satisfies the equation \[\frac{3 - 4ix}{3 + 4ix} = a - ib (a, b \in \mathbb{R}), if a^2 + b^2 =\]
Which of the following is correct for any two complex numbers z1 and z2?
Find a and b if (a – b) + (a + b)i = a + 5i
Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i
Express the following in the form of a + ib, a, b ∈ R, i = `sqrt(−1)`. State the values of a and b:
`("i"(4 + 3"i"))/((1 - "i"))`
If z1 and z2 both satisfy `z + barz = 2|z - 1|` arg`(z_1 - z_2) = pi/4`, then find `"Im" (z_1 + z_2)`.
State True or False for the following:
The order relation is defined on the set of complex numbers.
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
