How do you simplify #(-10+11i)(4+2i)-(4i)(-8i)(1-8i)#?

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Answer 1 · 2016-11-08T04:34:08

#-94+280i#

Simplify #(-10+11i)(4+2i)-(4i)(-8i)(1-8i)#

Let's start by multiplying #(-10+11i)(4+2i)#

Multiply each term in the first binomial by each term in the second.

#-40-20i+44i+22i^2 - (4i)(-8i)(1-8i)#

Combine like terms and recall that #i^2=-1#

#-40+24i+22(-1)-(4i)(-8i)(1-8i)#

#-40+24i-22-(4i)(-8i)(1-8i)#

#-62+24i-(4i)(-8i)(1-8i)#

Now let's multiply #(4i)(-8i)#

#-62+24i-(-32i^2)(1-8i)#

#-62+24i+32i^2(1-8i)#

Again, recall that #i^2=-1#

#-62+24i+32(-1)(1-8i)#

#-62+24i-32(1-8i)#

Distribute the #-32#

#-62+24i-32+256i#

Combine like terms

#-94+280i#