Explain how to multiply complex numbers and give an example. 3+2i

Stefan Hendricks

Stefan Hendricks

Answered question

2021-12-30

Explain how to multiply complex numbers and give an example.
3+2i and 23i

Answer & Explanation

yotaniwc

yotaniwc

Beginner2021-12-31Added 34 answers

Step 1
If the two complex numbers are a+bi and c+di, the multiplication of these complex numbers is (a+bi)(c+di)
Simplify (a+bi)(c+di) using distributive property and reduce thr powers of i's using i2=1
Step 2
For examples consider two complex numbers as 3+2i and 23i
The multiplication of these two complex numbers is,
(3+2i)(23i)=3×2+3(3i)+(2i)×2+(2i)(3i)
=69i+4i6i2
=65i6(1)
=65i+6
=125i
Therefore, the multiplication of complex numbers 3+2i and 23i is 125i
Stuart Rountree

Stuart Rountree

Beginner2022-01-01Added 29 answers

Step 1
Given complex numbers: 3+2i and 23i
Equation: (3+2i)(23i)
Apply complex arithmetric rule: (a+bi)(c+di)=(acbd)+(ad+bc)i
a=3
b=2
c=2
d=3
=(3×22(3))+(3(3)+2×2)i
3×22(3)=12
3(3)+2×2=5
=125i
Vasquez

Vasquez

Expert2022-01-08Added 669 answers

Step 1
1) Complex number: 3+2i
2) Complex number: 2-3i
Multiple: the result of step 1×the result of step 2
=(3+2i)×(2-3i)
3×2+3×(-3i)+2i×2+2i×(-3i)
=6-9i+4i-6i2
=6-9i+4i+6
=6+6+i(-9+4)
=12-5i

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