Express the following in the form of a + ib, a, b ∈ R, i = -1. State the values of a and b: (2 + 3i)(2 – 3i) - Mathematics and Statistics

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)

Sum

(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

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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 2) vi) | Page 37

Write the conjugates of the following complex numbers: 3 – i

Write the conjugates of the following complex numbers: 5i

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:

(1 + 2i)(– 2 + 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 + sqrt(-3))/(4 + sqrt(-3))`

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

Find the value of 1 + i² + i⁴ + i⁶ + i⁸ + ... + i²⁰.

Show that `(−1 + sqrt3 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.

Evaluate the following:

`i^35`