If z1=3-i and z2 = -3+i , find Re(z1z2/z1).
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Answers
Step-by-step explanation:
−9+3+3+1
2 Collect like terms.
\frac{(-9+1)+(3\imath +3\imath )}{3-\imath }
3−
(−9+1)+(3+3)
3 Simplify (-9+1)+(3\imath +3\imath )(−9+1)+(3+3) to -8+6\imath−8+6.
\frac{-8+6\imath }{3-\imath }
3−
−8+6
4 Rationalize the denominator: \frac{-8+6\imath }{3-\imath } \cdot \frac{3+\imath }{3+\imath }=\frac{-24-8\imath +18\imath -6}{{3}^{2}-{\imath }^{2}}
3−
−8+6
⋅
3+
3+
=
3
2
−
2
−24−8+18−6
.
\frac{-24-8\imath +18\imath -6}{{3}^{2}-{\imath }^{2}}
3
2
−
2
−24−8+18−6
5 Collect like terms.
\frac{(-24-6)+(-8\imath +18\imath )}{{3}^{2}-{\imath }^{2}}
3
2
−
2
(−24−6)+(−8+18)
6 Simplify (-24-6)+(-8\imath +18\imath )(−24−6)+(−8+18) to -30+10\imath−30+10.
\frac{-30+10\imath }{{3}^{2}-{\imath }^{2}}
3
2
−
2
−30+10
7 Simplify {3}^{2}3
2
to 99.
\frac{-30+10\imath }{9-{\imath }^{2}}
9−
2
−30+10
8 Use Square Rule: {i}^{2}=-1i
2
=−1.
\frac{-30+10\imath }{9-(-1)}
9−(−1)
−30+10
9 Remove parentheses.
\frac{-30+10\imath }{9+1}
9+1
−30+10
10 Simplify 9+19+1 to 1010.
\frac{-30+10\imath }{10}
10
−30+10
11 Factor out the common term 1010.
\frac{-10(3-\imath )}{10}
10
−10(3−)
12 Move the negative sign to the left.
-\frac{10(3-\imath )}{10}
−
10
10(3−)
13 Cancel 1010.
-(3-\imath )
−(3−)
14 Remove parentheses.
-3+\imath
−3+