Advertisements
Advertisements
प्रश्न
Express the given complex number in the form a + ib: `(1/5 + i 2/5) - (4 + i 5/2)`
Advertisements
उत्तर
`(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
संबंधित प्रश्न
Express the given complex number in the form a + ib: i9 + i19
Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)
Express the given complex number in the form a + ib: `(-2 - 1/3 i)^3`
Let z1 = 2 – i, z2 = –2 + i. Find Re`((z_1z_2)/barz_1)`
Let z1 = 2 – i, z2 = –2 + i. Find `"Im"(1/(z_1barz_1))`
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:
\[\frac{3 + 2i}{- 2 + i}\]
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:
\[(1 + 2i )^{- 3}\]
Find the real value of x and y, if
\[(1 + i)(x + iy) = 2 - 5i\]
If \[\left( \frac{1 - i}{1 + i} \right)^{100} = a + ib\] find (a, b).
Solve the system of equations \[\text { Re }\left( z^2 \right) = 0, \left| z \right| = 2\].
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.
If \[\left| z + 1 \right| = z + 2\left( 1 + i \right)\],find z.
Solve the equation \[\left| z \right| = z + 1 + 2i\].
Find the number of solutions of \[z^2 + \left| z \right|^2 = 0\].
Express the following complex in the form r(cos θ + i sin θ):
tan α − i
Express the following complex in the form r(cos θ + i sin θ):
1 − sin α + i cos α
Express \[\sin\frac{\pi}{5} + i\left( 1 - \cos\frac{\pi}{5} \right)\] in polar form.
If \[\left| z - 5i \right| = \left| z + 5i \right|\] , then find the locus of z.
Write the value of \[\arg\left( z \right) + \arg\left( \bar{z} \right)\].
If \[\left| z + 4 \right| \leq 3\], then find the greatest and least values of \[\left| z + 1 \right|\].
If n ∈ \[\mathbb{N}\] then find the value of \[i^n + i^{n + 1} + i^{n + 2} + i^{n + 3}\] .
The principal value of the amplitude of (1 + i) is
If \[z = \left( \frac{1 + i}{1 - i} \right)\] then z4 equals
If \[x + iy = \frac{3 + 5i}{7 - 6i},\] then y =
The amplitude of \[\frac{1 + i\sqrt{3}}{\sqrt{3} + i}\] is
If \[f\left( z \right) = \frac{7 - z}{1 - z^2}\] , where \[z = 1 + 2i\] then \[\left| f\left( z \right) \right|\] is
Which of the following is correct for any two complex numbers z1 and z2?
If the complex number \[z = x + iy\] satisfies the condition \[\left| z + 1 \right| = 1\], then z lies on
Find a and b if (a+b) (2 + i) = b + 1 + (10 + 2a)i
Find a and b if `1/("a" + "ib")` = 3 – 2i
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)`
If z1 = 3 – 2i and z2 = –1 + 3i, then Im(z1z2) = ______.
State true or false for the following:
If a complex number coincides with its conjugate, then the number must lie on imaginary axis.
The real value of θ for which the expression `(1 + i cos theta)/(1 - 2i cos theta)` is a real number is ______.
Show that `(-1+sqrt3i)^3` is a real number.
