# Simplify the following and express in the form a + ib: 4+3i1-i - Mathematics and Statistics

Sum

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

(4 + 3"i")/(1 - "i")

#### Solution

(4 + 3"i")/(1 - "i") = ((4 + 3"i")(1 + "i"))/((1 - "i")(1 + "i")

= (4 + 4"i" + 3"i" + 3"i"^2)/(1 - "i"^2)

= (4 + 7"i" + 3(-1))/(1 - (-1)      ...[∵ i2 = – 1]

= (1 + 7"i")/2

= 1/2+7/2"i".

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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. (vi) | Page 42