Question

Simplify the multiplication of complex numbers: $\left( {x,y} \right) \times \left( {1,0} \right)$
A) $\left( { - x, - y} \right)$
B) $\left( {y,x} \right)$
C) $\left( {x,y} \right)$
D) None of these

Answer 1

Hint : We will solve this question by first taking $\left( {x,y} \right)$ as $\left( {x + iy} \right)$ and $\left( {1,0} \right)$ as $\left( {1 + i0} \right).$ Then on multiplying both the complex numbers we will get the required answer.

Complete step-by-step answer :
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i represents the imaginary unit, satisfying the equation i2 = −1. Because no real number satisfies this equation, i is called an imaginary number.

We have been given complex numbers and we need to simplify the multiplication $\left( {x,y} \right) \times \left( {1,0} \right).$
So, $\left( {x,y} \right)$ can be written as $\left( {x + iy} \right)$
And $\left( {1,0} \right)$ can be written as $\left( {1 + i0} \right)$
Now, we can write $\left( {x,y} \right) \times \left( {1,0} \right)$ as $\left( {x + iy} \right) \times \left( {1 + i0} \right)$
So, $\left( {x,y} \right) \times \left( {1,0} \right){\text{ }} = {\text{ }}\left( {x + iy} \right) \times \left( {1 + i0} \right)$

{\left( {x,y} \right) \times \left( {1,0} \right){\text{ }} = {\text{ }}\left( {x + iy} \right) \times \left( 1 \right)} \\\ {\left( {x,y} \right) \times \left( {1,0} \right){\text{ }} = {\text{ }}\left( {x + iy} \right)} \\\ {\left( {x,y} \right) \times \left( {1,0} \right){\text{ }} = {\text{ }}\left( {x,y} \right)} \end{array}$$ **So, the correct answer is “Option C”.** **Note** : Complex numbers are a combination of real and imaginary numbers. And when two complex numbers multiply, the first complex number gets multiplied by each part of the second complex number.