Complex number in rectangular form What is (1+2j) + (1+3j)? Your answer should contain three significant figures.

vestirme4

vestirme4

Answered question

2021-05-29

Complex number in rectangular form What is (1+2j) + (1+3j)? Your answer should contain three significant figures.

Answer & Explanation

StrycharzT

StrycharzT

Skilled2021-05-30Added 102 answers

Sum of complex numbers (a1+b1i)+(a2+b2i)=(a1+a2)+(b1+b2)i=a+bi
(1+2i)+(1+3i)=(1+1)+(2+3)i=2+5i this is the binomial form
Then find r and θ
r=a2+b2=22+52=29
if a and b are possitive then
θ=tan1(ba)=tan1(52)=68.2
Rectangle form
z=r(cos(θ)+sin(θ)i)
then z=29(cos(68.2)+sin(68.2)i)
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

RizerMix

RizerMix

Expert2023-05-25Added 656 answers

Answer:
(1+2j)+(1+3j)=2+5j
Explanation:
Given:
(1+2j)+(1+3j)
We can group the real and imaginary parts:
(1+1)+(2j+3j)
Simplifying the real part:
1+1=2
Simplifying the imaginary part:
2j+3j=5j
Combining the real and imaginary parts, we get the result:
2+5j
Therefore, (1+2j)+(1+3j)=2+5j.
Don Sumner

Don Sumner

Skilled2023-05-25Added 184 answers

Let's start by adding the real parts together:
(1+2j)+(1+3j)=1+1+2j+3j
Next, we add the imaginary parts together:
=2+5j
Therefore, the sum of (1+2j)+(1+3j) is 2+5j.
In rectangular form, the complex number 2+5j can be represented as 2+5i, where i is also used to denote the imaginary unit.
nick1337

nick1337

Expert2023-05-25Added 777 answers

To solve the expression (1+2j)+(1+3j) in rectangular form, we simply add the real parts and the imaginary parts separately. The real part is obtained by adding the real parts of the complex numbers, and the imaginary part is obtained by adding the imaginary parts.
Let's break down the calculation:
Real part: 1+1=2
Imaginary part: 2j+3j=5j
Putting it all together, the sum of (1+2j)+(1+3j) is 2+5j.
Hence, the result in rectangular form is 2+5j.

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