How do you divide #( i+8) / (5i +5 )# in trigonometric form?

1 Answer
Yonas Yohannes
Mar 19, 2016

#C_3 = (40+5i-40i+5)/(25+25)= (45-35i)/50= 1/10(9-7i)#

Explanation:

Given the complex set #C_1 =( i+8)# and #C_2=(5i +5 )#
Required: #( i+8)/(5i +5 )#
Solution: Use complex conjugate of #C_2#, #bar(C_2)#to perform complex number division.
The product of a complex number #C# with it's conjugate #bar(C)# is: #R = C*bar(C) = (a+bi)(a-bi) =a^2+b^2#, a real number.
Thus multiplying top and bottom by #bar(C_2) = 5-5i#
#C_3 = (C_1*bar(C_2))/(C_2*bar(C_2)) = ((i+8)(5-5i))/((5+5i)*(5-5i))#

#C_3 = (40+5i-40i+5)/(25+25)= (45-35i)/50= 1/10(9-7i)#

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