Can you simplify imaginary numbers

These will cancel each other out. This will always happen as a result of multiplying by the conjugate. The imaginary terms of the denominator should always cancel and disappear. Return to complex number format. Recognize that the single denominator applies equally to both portions of the numerator.

Split the numerator apart to create a standard complex number. What if there's only 1 number for the denominator when it comes to complex numbers?

What would the conjugate be for the denominator? Here, your denominator has a real number of 0 and a complex number of You multiply with that and it cancels out the 'i' in the denominator.

Yes No. Not Helpful 1 Helpful 7. Not Helpful 2 Helpful 0. Orlando Huang. You can't sumplify, you can only solve. Not Helpful 0 Helpful 1. Bella Johnston. When simplifying an equation like this, you need to combine like terms. Like terms are numbers that have the same coefficient in this case, the letter "i". So, first should combine like terms everything with the letter "i".

Now solve like terms in each set of parenthesis. Now drop the parentheses because there are no more like terms in them and solve! Include your email address to get a message when this question is answered. Submit a Tip All tip submissions are carefully reviewed before being published. Related wikiHows How to. Algebra often involves simplifying expressions, but some expressions are more confusing to deal with than others. The general form for a complex number shows their structure:.

So an example complex number is:. To add and subtract complex numbers, simply add or subtract the real and imaginary parts separately. So for example:. Dividing complex numbers involves multiplying the numerator and denominator of the fraction by the complex conjugate of the denominator. The complex conjugate just means the version of the complex number with the imaginary part reversed in sign. The imaginary unit, j, is the square root of Hence the square of the imaginary unit is This follows that:.

Understanding the powers of the imaginary unit is essential in understanding imaginary numbers. Following the examples above, it can be seen that there is a pattern for the powers of the imaginary unit. It always simplifies to -1, - j , 1, or j.

A simple shortcut to simplify an imaginary unit raised to a power is to divide the power by 4 and then raise the imaginary unit to the power of the reminder. Simply put, a conjugate is when you switch the sign between the two units in an equation.

The conjugate of a complex number would be another complex number that also had a real part, imaginary part, the same magnitude.

However, it has the opposite sign from the imaginary unit. They are important in finding the roots of polynomials. The above expression is a complex fraction where the denominator is a complex number. As it is, we can't simplify it any further except if we rationalized the denominator. The concept of conjugates would come in handy in this situation. But then people researched them more and discovered they were actually useful and important because they filled a gap in mathematics And that is also how the name " Real Numbers " came about real is not imaginary.

Those cool displays you see when music is playing? Yep, Complex Numbers are used to calculate them!