Advertisements
Advertisements
प्रश्न
Find the modulus of the following complex numbers
`(2 - "i")/(1 + "i") + (1 - 2"i")/(1 - "i")`
उत्तर
Let z = `(2 - "i")/(1 + "i") + (1 - 2"i")/(1 - "i")`
= `((2 - "i")(1 - "i") + (1 - 2"i")(1 + "i"))/((1 + "i")(1 - "i"))`
= `(4 - 4"i")/2`
= 2 – 2i
Modulus of z = |z|
= `sqrt(4 + 4)`
= `sqrt(8)`
= `2sqrt(2)`
APPEARS IN
संबंधित प्रश्न
Find the modulus of the following complex numbers
2i(3 – 4i)(4 – 3i)
For any two complex numbers z1 and z2, such that |z1| = |z2| = 1 and z1 z2 ≠ -1, then show that `(z_1 + z_2)/(1 + z_1 z_2)` is real number
Which one of the points 10 – 8i, 11 + 6i is closest to 1 + i
If |z| = 3, show that 7 ≤ |z + 6 – 8i| ≤ 13
If |z| = 1, show that 2 ≤ |z2 – 3| ≤ 4
If |z| = 2 show that the 8 ≤ |z + 6 + 8i| ≤ 12
If the area of the triangle formed by the vertices z, iz, and z + iz is 50 square units, find the value of |z|
Show that the equation `z^3 + 2bar(z)` = 0 has five solutions
Find the square roots of 4 + 3i
Find the square roots of – 6 + 8i
Find the square roots of – 5 – 12i
Choose the correct alternative:
If = `((sqrt(3) + "i")^3 (3"i" + 4)^2)/(8 + 6"i")^2`, then |z| is equal to
Choose the correct alternative:
If z is a non zero complex number, such that 2iz2 = `bar(z)` then |z| is
Choose the correct alternative:
If |z – 2 + i| ≤ 2, then the greatest value of |z| is
Choose the correct alternative:
If (1 + i)(1 + 2i)(1 + 3i) ……. (l + ni) = x + iy, then 2.5.10 …… (1 + n2) is
Choose the correct alternative:
If α and β are the roots of x² + x + 1 = 0, then α2020 + β2020 is
Choose the correct alternative:
The value of `((1 + sqrt(3)"i")/(1 - sqrt(3)"i"))^10` is
