To solve, you must remember the basic rules for i exponents.

Given the prior, simply plug into the given expression and combine like terms.

In order to determine if a quadratic equation  will have real-valued or complex-valued solutions compute the discriminate: 

If the discriminate is negative, we will have complex-valued solutions. If the discriminate is positive, we will have real-valued solutions. 

This arises from the fact that the quadratic equation has the square-root term, 

Evaluate the discriminate for 

 -79<0 so the quadratic has complex roots for . 

Evaluate the discriminate for 

The discriminate is positive, therefor the quadratic has real roots for 

Recall that , , and .

Each imaginary term can then be factored by using .

Replace the numerical values for each term.

The answer is:  

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the negative:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 2+4i

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 10-4i

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 10+2i

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 7+18i

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 9+2i

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of -1+9i

When simplifying expressions with complex numbers, use the same techniques and procedures as normal. 

Distribute the sign to the terms in parentheses:

Combine like terms- combine the real numbers together and the imaginary numbers together:

This gives a final answer of 10-4i