# 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

Sum

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)

#### Solution

(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

Concept: Conjugate of a Complex Number
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Exercise 3.1 | Q 2. (vi) | Page 37