How do you divide \frac{3i}{1+i}+\frac{2}{2+3i}?

tearstreakdl

tearstreakdl

Answered question

2022-01-16

How do you divide 3i1+i+22+3i?

Answer & Explanation

Lindsey Gamble

Lindsey Gamble

Beginner2022-01-17Added 38 answers

3i1+i+22+3i
=3i(1i)(1+i)(1i)+2(23i)(2+3i)(23i)
=3i3i21i2+46i49i2
=3i3(1)1(1)+46i49(1) [as, i2=1]
=3i+31+1+46i4+9
=3i+32+46i13
=32i+32+413613i
=2726i+4726
Anzante2m

Anzante2m

Beginner2022-01-18Added 34 answers

Get a common denominator.
=3i(2+3i)(1+i)(2+3i)+2(1+i)(1+i)(2+3i)
=6i+9i22+5i+3i2+2+2i2+5i+3i2
=2+8i+9i22+5i+3i2
This can be simplified since i2=1.
=2+8i92+5i3
=7+8i1+5i
Now, multiply by the complex conjugate of the denominator.
=7+8i1+5i(15i15i)
=7+27i40i2125i2
=7+27i+401+25
=47+27i26
=4726+2726i

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