Rewrite negative square roots in terms of the square root of negative one. For instance, sqrt(-36), which is read as the square root of -36, is rewritten as sqrt(36) x sqrt(-1) read the square root of 36 times the square root of -1.
Replace the square root of -1 with the value i where appropriate. In the previous step, you rewrote sqrt(-36) as sqrt(36) x sqrt(-1). Now, for each sqrt(-1) written replace the term with the variable i. This term now becomes sqrt(36) x i.
Combine all like terms. If the equation has multiple terms with an i value, then combine all terms of i. For instance, the equation 6 - 3i + 2i - 4i is rewritten as 6 - 5i. All terms with an i are combined to result in -5i. The i is treated as a simple variable, so like terms can be combined.
Replace i^2 with the value of -1. For any term i x i, denoted by i^2 and read as i-squared, replace that variable with the value -1 since i x i = -1, the substitution property in mathematics allows this step to be valid. For instance, 6 + i^2 is rewritten as 6 + (-1).
Simplify. Once values of i^2 are replaced with the value -1, combine all real numbers to simplify. The step above showed that 6 + i^2 is rewritten as 6 + (-1), which can be simplified to 5. If you are unable to simplify, proceed to the next step.
Rewrite higher power of i in terms of i^2. If there is a term with i to a power higher than two, rewrite the term to use i^2. For instance, i^3 can be rewritten as i x i^2. Additionally, i^4 can be rewritten as i^2 x i^2.
Repeat Steps 4 to 6 until the equation only has terms of i. The final equation should not have any higher power of i. All numbers should be real numbers or written in terms of i. If there are any terms with i to a power greater than one, repeat the steps until the highest power of i is one.