Question 1041241
# 1) Correct


# 2) Correct


# 3) The answer is actually {{{-1/10 + expr(1/5)i}}}. See below



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Steps for # 3



{{{(1+2i)/(6-8i)}}}



{{{((1+2i)/(6-8i))*((6+8i)/(6+8i))}}} Multiply by {{{(6+8i)/(6+8i)}}} which is a fancy form of 1



{{{((1+2i)(6+8i))/((6-8i)(6+8i))}}} Combine fractions



{{{(6+8i+12i+16i^2)/(6^2-(8i)^2)}}} Expand



{{{(6+8i+12i+16i^2)/(36-64i^2)}}} Square each term



{{{(6+8i+12i+16(-1))/(36-64(-1))}}} Use the idea that {{{i^2 = -1}}}



{{{(6+8i+12i-16)/(36+64)}}}



{{{(-10+20i)/100}}}



{{{(-10)/100+(20i)/100}}} Break up the fraction



{{{-1/10+expr(1/5)i}}} Reduce





So {{{(1+2i)/(6-8i)}}} is equivalent to {{{-1/10+expr(1/5)i}}}


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So again, the answer for problem #3 is {{{-1/10 + expr(1/5)i}}}