What does it mean to have complex solutions?

1) If the discriminant is less than zero, the equation has two complex solution(s). 2) If the discriminant is equal to zero, the equation has one repeated real solution(s). 3) If the discriminant is greater than zero, the equation has. two distinct real. solution(s).

How do you find complex solutions?

To solve for the complex solutions of an equation, you use factoring, the square root property for solving quadratics, and the quadratic formula.

What is the difference between real and complex solutions?

A real number can be a rational and irrational number and can have any value on the number line. A complex number exists in the form a + ib where i is used for denoting the imaginary part and a and b denote the real numbers.

How many complex solutions does a polynomial have?

Every polynomial equation P(x) = 0 of any degree ≥ 1 with complex number coefficients has at least one complex number solution.

What is a complex equation?

A complex equation is an equation that involves complex numbers when solving it. A complex number is a number that has both a real part and an imaginary part. It is written in this form: In the above equation, a and b both stand for numbers. For example, <4+3i> is a complex number.

What is complex equation?

Is 4 is a complex number?

The complex number is the combination of a real number and imaginary number. An example of a complex number is 4+3i. Here 4 is a real number and 3i is an imaginary number.

Is 3 a complex number?

In this complex number, 3 is the real number and 5i is the imaginary number. Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Because either part could be 0, technically any real number or imaginary number can be considered a complex number.

Is 5 a complex number?

Solution In this example, there is no real part. In other words, the real part is 0. The imaginary part is 5. In fact all real numbers can be thought of as complex numbers which have zero imaginary part.

What is 3/8 as a complex number?

The fraction 3/8 is a number made up of a 3 and an 8. We know it means “3 of 8 equal parts”. Well, a Complex Number is just two numbers added together (a Real and an Imaginary Number). So, a Complex Number has a real part and an imaginary part. But either part can be 0, so all Real Numbers and Imaginary Numbers are also Complex Numbers.

What is the result of multiplying complex conjugates?

The real number that results from multiplying complex conjugates: ( a + b i) ( a − b i) = a 2 + b 2. ( a + b i) ( a − b i) = a 2 + b 2. Note that the result does not involve the imaginary unit; hence the result is real. This leads us to the very useful property:

When to use re() and IM() for complex numbers?

The general rule is: DONE! We often use z for a complex number. And Re () for the real part and Im () for the imaginary part, like this: The beautiful Mandelbrot Set (pictured here) is based on Complex Numbers.

How do you use complex numbers to solve a quadratic equation?

The result of adding, subtracting, multiplying, and dividing complex numbers is a complex number. Use complex numbers to describe solutions to quadratic equations that are not real. Rewrite in terms of i. Perform the operations. Solve by extracting the roots and then solve by using the quadratic formula.