How do I simplify this?
#(4+2i)/(-4-6i)#
2 Answers
Explanation:
Multiply the Numerator and Denominator by the Conjugate of the Denominator.
The Conjugate is exactly like the Denominator except the sign on the imaginary number is different.
Multiply by Distribution on Numerator and Denominator.
Note:
Combine Like Terms and Replace
Simplify by Dividing all Numbers by 4:
Given
#(4+2i)/(-4-6i)#
From inspection we see that both in the numerator and denominator factor
#-(2(2+i))/(2(2+3i))#
#=>-((2+i))/((2+3i))#
Multiplying and dividing with complex conjugate of denominator we get
#-((2+i))/((2+3i))xx(2-3i)/(2-3i)#
#=>-((2+i)(2-3i))/((2)^2-(3i)^2)#
#=>-(4-6i+2i-3i^2)/((2)^2-(3i)^2)#
#=>-(7-4i)/(13)#
#=>(4i-7)/(13)#