Question

(√5+7i)(√5-7i)^2
$a + ib$
​

Answer 1

Step-by-step explanation:

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Answer 2

The answer is 54√5 - 378i

Given: (√5+7i)(√5-7i)²  

To find: Expressing (√5+7i)(√5-7i)² in the form of  $a+ib$  

Solution:

Given (√5+7i)(√5-7i)²  

⇒ (√5+7i)(√5-7i)(√5-7i)     [ ∵ a² = a × a ]

⇒ [ (√5+7i)(√5-7i) ] (√5-7i)    

⇒  [ $(\sqrt{5} )^{2} - (7i)^{2}$ ] (√5-7i)    [ ∵ (a+b)(a-b) = a² - b² ]

⇒  [ 5 - 49 (-1) ] (√5-7i)      [ ∵  i² = -1 ]

⇒  [ 5+49 ] (√5-7i)  

⇒   54 (√5-7i)  = 54√5 - 378i  

⇒   $a+ib$  = 54√5 - 378i

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