This is about understanding real and complex numbers.
Complex Numbers; 7 - 5i, √-6, 0 + 9i, , -i² + i³
Real Numbers; i⁶, 2 - 7i², -12, √(-5)²
Let's first define real and complex numbers.
- A real number is any number that can be represented on a number line. That means it can be a rational or an irrational number.
- Meanwhile, Complex numbers are numbers that cannot be represented on a number line but instead take the form of x + yi, where x and y represent real numbers while the letter i next to y represents an imaginary part.
The. expressions we are given are;
i⁶, 2 - 7i², 7 - 5i, √-6, 0 + 9i, -12, √(-5)², -i² + i³
- i⁶ can be expressed as; i² × i² × i² . Now the square of an imaginary number is -1. Thus; i² × i² × i² = -1 × -1 × -1 = -1 which is a real number.
- 2 - 7i²; we know that the square of an imaginary number is -1, Thus;
2 - 7i² = 2 - 7(-1) = 9 which is a real number.
- 7 - 5i; This is a complex number because it is of the form x + yi.
- √-6; This is a complex number because negative roots are only imaginary and not possible.
- 0 + 9i; This is a complex number because it is of the form x + yi.
- -12 is a real number as it can be represented on the number line.
- √(-5)² = √25 = 5 which is a real number
- -i² + i³ can be expressed as; -i² + i(i²). Square of imaginary number = -1. Thus; -i² + i(i²) = 1 - 1i. This is a complex number.
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