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Catherene Roman

Answered question

2022-08-28

Mr Solver

Skilled2023-06-05Added 147 answers

a. To find the sum of the complex numbers

(\sqrt{2}, - 1)

and

(1, - \sqrt{2})

, we add the real parts and the imaginary parts separately:
Real part:

\sqrt{2} + 1

Imaginary part:

- 1 + (- \sqrt{2})

Therefore, the sum is

(\sqrt{2} + 1, - 1 - \sqrt{2})

.
b. To find the sum of the complex numbers

(3, - 1)

and

(\frac{1}{5}, \frac{1}{10})

, we add the real parts and the imaginary parts separately:
Real part:

3 + \frac{1}{5}

Imaginary part:

- 1 + \frac{1}{10}

Therefore, the sum is

(\frac{16}{5}, - \frac{9}{10})

.
c. The sum of complex numbers

(a, b)

and

(c, d)

(a + c, b + d)

.
d. To find the sum of the complex numbers

(x^{2} - 2, x + 2)

and

(1, x - 2)

, we add the real parts and the imaginary parts separately:
Real part:

(x^{2} - 2) + 1

Imaginary part:

(x + 2) + (x - 2)

Simplifying, we have:
Real part:

x^{2} - 1

Imaginary part:

2 x

Therefore, the sum is

(x^{2} - 1, 2 x)

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