Write the conjugates of the following complex numbers: 5-i - Mathematics and Statistics

Write the conjugates of the following complex numbers: `sqrt(5) - "i"`

Sum

Conjugate of `sqrt(5) - "i" "is" sqrt(5) + "i"`

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Conjugate of a Complex Number

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Chapter 3: Complex Numbers - EXERCISE 3.1 [Page 37]

Chapter 3 Complex Numbers
EXERCISE 3.1 | Q 1) vi) | Page 37

Write the conjugates of the following complex numbers: `sqrt(2) + sqrt(3) "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"))`

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: (2 + 3i)(2 – 3i)

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 1 + i² + i⁴ + i⁶ + i⁸ + ... + i²⁰.

Show that `(-1 + sqrt(3) i)^3` is a real number.

Show that `(−1 + sqrt3 i)^3` is a real number.

Show that `(−1+ sqrt3 i)^3` is a real number.

Show that `(−1 + sqrt(3) i)^3`is a real number.

Show that `(-1 + sqrt3"i")^3` is a real number.

Evaluate the following:

`i^35`

Show that `(-1 + sqrt3i)^3` is a real number.

Simplify the following and express in the form a+ib.

`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`