How do you simplify (4+ 3i) div (2 - i)(4+3i)÷(2−i)?

1 Answer
sente
Jul 13, 2016

(4+3i)/(2-i)=1+2i4+3i2−i=1+2i

Explanation:

The complex conjugate of a complex number a+bia+bi is denoted bar(a+bi)¯¯¯¯¯¯¯¯¯¯a+bi and is given by bar(a+bi) = a-bi¯¯¯¯¯¯¯¯¯¯a+bi=a−bi. A useful property of the complex conjugate is that for any complex number zz, we have zbar(z) in RR. We will use this property to simplify the given expression by multiplying the numerator and denominator by the conjugate of the denominator.

(4+3i)/(2-i) = ((4+3i)(2+i))/((2-i)(2+i))

=(8+6i+4i-3)/(4+2i-2i+1)

=(5+10i)/5

=1+2i

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