# Simplify the following and express in the form a + ib: 5+7i4+3i+5+7i4-3i - Mathematics and Statistics

Sum

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

(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")

#### Solution

(5 + 7"i")/(4 + 3"i") + (5 + 7"i")/(4 - 3"i")

= (5 + 7"i")[1/(4 + 3"i") + 1/(4 - 3"i")]

= (5 + 7"i") [(4 - 3"i" + 4 + 3"i")/((4 + 3"i")(4 - 3"i"))]

= (5 + 7"i") [8/(16 - 9"i"^2)]

= (5 + 7"i") [8/(16 - 9(-1))]      ...[∵ i2 = – 1]

= (8(5 + 7"i"))/25

= (40 + 56"i")/25

= 40/25 + 56/25"i"

= 8/5 + 56/25"i".

Concept: Algebra of Complex Numbers
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 3 Complex Numbers
Miscellaneous Exercise 3 | Q 3. (x) | Page 43