Question

(2+√-4) (3 +5i)(-4-i)

Answer 1

`32-60i`

Explanation:

Given expression:

`(2+√(-4))(3 +5i)(-4-i)`

`\textsf{Rewrite $√(-4)$ as $√(4 \cdot -1)$}:`

`\implies (2+√(4 \cdot -1))(3 +5i)(-4-i)`

`\textsf{Apply radical rule} \quad √(ab)=√(a)√(b):`

`\implies (2+√(4)√(-1))(3 +5i)(-4-i)`

`\implies (2+2√(-1))(3 +5i)(-4-i)`

`\textsf{Apply imaginary number rule} \quad √(-1)=i:`

`\implies (2+2i)(3 +5i)(-4-i)`

Multiply:

`\implies (6+16i+10i^2)(-4-i)`

`\implies -24-6i-64i-16i^2-40i^2-10i^3`

`\implies -24-70i-56i^2-10i^3`

`\textsf{Apply imaginary number rule} \quad i^2=-1:`

`\implies -24-70i-56(-1)-10(-1)i`

Simplify:

`\implies -24-70i+56+10i`

`\implies 32-60i`

Answer 2

• 
  `32-60i`

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Simplify the expression in below steps:

• 
  `(2+√(-4) ) (3 +5i)(-4-i)=`
• 
  `(2+√(-1*4) ) (3 +5i)(-4-i)=`
• 
  `(2+2i ) (3 +5i)(-4-i)=`
• 
  `2(1+i ) (3 +5i)(-4-i)=`
• 
  `2(1+i ) (3(-4) -3i+5i(-4)-5i*i)=`
• 
  `2(1+i ) (-12 -3i-20i-5(-1))=`
• 
  `2(1+i ) (-12 -23i+5)=`
• 
  `2(1+i ) (-7 -23i)=`
• 
  `2(-7 -23i -7i-23i*i)=`
• 
  `2(-7 -30i +23)=`
• 
  `2(16 -30i)=`
• 
  `32-60i`