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Is every real number a complex number?
A complex number is a number of the form a + bi, where a and b are real numbers and i is the principal square root of -1. In the special case where b=0, a+0i=a. Hence every real number is also a complex number. And in the special case where a=0, we call those numbers pure imaginary numbers. Note that 0=0+0i, therefore 0 is both a real number and a pure imaginary number. Do not confuse the complex numbers with the pure imaginary numbers. Every real number is a complex number and every pure imaginary number is a complex number also.
Which equation has imaginary roots a.x2-1 equals 0 b.x2-2 equals 0 c.x2 plus x plus 1 equals 0 d.x2-x-1 equals 0?
To find which has imaginary roots, use the discriminant of the quadratic formula (b2 - 4ac) and see if it's less than 0. (The quadratic formula corresponds to general form of a quadratic equation, y = ax2 + bx + c)A) x2 - 1 = 0= 0 - 4(1)(-1) = 4Therefore, the roots are not imaginary.B) x2 - 2 = 0= 0 - 4(1)(-2) = 8Therefore, the roots are not imaginary.C) x2 + x + 1 = 0= 1 - 4(1)(1) = -3Therefore, the roots are imaginary.D) x2 - x - 1 = 0= 1 - 4(1)(-1) = 5Therefore, the roots are not imaginary.The equation x2 + x + 1 = 0 has imaginary roots.
What two integers lie between the square root of negative 55?
The square roots of negative 55 are the imaginary numbers -7.4162*i and 7.4162*i where i is the square root of -1. There can be only one integer between any two imaginary numbers and that is 0.
What is the quare root of -1?
The square root of -1 is not a real number like -2.5, 0, or 5. Instead, it is and imaginary number, i, and i = the square root of -1. The answer is imaginary because you can never take a real number, square it, and get a negative number. However, i^2 = -1.
Are square roots real numbers?
Yes, if the number whose square root we are taking is greater than 0. Only if you try to take the square root of a negative number will you get back an imaginary number. Square roots are often irrational, but that's different from real versus imaginary.
