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Express the following in the form of a +...

Express the following in the form of a + ib .
(i) ` ( 1/2 + 3i)^(2)`
(ii) ( 2+ 3i) ( 2-3i)

Text Solution

Verified by Experts

(i) ` ( 1/2 + 3i)^(2)`
` = (1/2)^(2) + ( 3i)^(2) + 2"" 1/2 3i`
` = 1/4 + 9i^(2) + 3i`
`= ( -35)/4 + 3i`
(ii) ( 2 + 3i) ( 2-3i)
= `( 2)^(2) - ( 3i)^(2)`
`= 4 - 9i^(2)`
13 + 0 i
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