Find the sum and the product of the complex numbers

kloseyq

kloseyq

Answered question

2021-12-26

Find the sum and the product of the complex numbers 32i and 3+5i.

Answer & Explanation

temzej9

temzej9

Beginner2021-12-27Added 30 answers

Step 1
Consider the complex numbers 32i and 3+5i.
To find the sum of the complex numbers, add/subtract the real part with real and the imaginary part with the imaginary part.
So the sum of the complex numbers is
(32i)+(3+5i)=32i3+5i
=332i+5i
=0+3i
=3i
Thus, the sum of the complex numbers is 3i.
Step 2
To find the product of the complex number, use FOIL method to multiply the binomials and simplify further as shown below
(32i)(3+5i)=3×(3)+3×(5i)2i×(3)2i×(5i)
=9+15i+6i10i2
=9+21i10(1)(i2=1)
=9+21i+10
=1+21i
Thus, the product of the complex numbers is 1+21i
limacarp4

limacarp4

Beginner2021-12-28Added 39 answers

Step 1
Complex number:
1) 32i
2) 3+5i
Add: (1)+(2)=(32i)+(3+5i)=(33)+(2+5)i=3i
Step 2
(32i)(3+5i)
Apply complex arithmetric rule:
(a+bi)(c+di)=(acbd)+(ad+bc)i
a=3, b=2, c=3, d=5
=(3(3)(2)×5)+(3×5+(2)(3))i
3(3)(2)×5=1
3×5+(2)(3)=21
=1+21i
Vasquez

Vasquez

Expert2022-01-08Added 669 answers

Step 1
(32i)+(3+5t)
Group the real part and the imaginary part of the complex number
(a+bi)±(c+dt)=(a±c)+(b±d)i=(33)+(2+5)i33=02+5=3=0+3i=0+3iStep 2Multiple: (32i)×(3+5i)=3×(3)+3×5i+(2i)×(3)+(2i)×5i=9+15i+6i10i2=9+15i+6i+10=9+10+i(15+6)=1+21i

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