Common Core: High School - Number and Quantity : The Complex Number System
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Example Questions
Example Question #1 : Complex Number Form: Ccss.Math.Content.Hsn Cn.A.1
Simplifying the following.
This question tests one's ability to perform arithmetic operations on complex numbers. Questions like this introduces and builds on the concept of complex numbers. Recall that a complex number by definition contains a negative square. In mathematical terms this is expressed as follows.
Performing arithmetic operations on complex numbers relies on the understanding of the various algebraic operations and properties (distributive, associative, and commutative properties) as well as the imaginary, complex number 
For the purpose of Common Core Standards, "know there is a complex number 
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Perform multiplication between the two terms.
Recall that multiplication between two radicand terms (terms under the square root sign), can be combined as one using the communicative property with multiplication.
Step 2: Factor the two term in the expression.
Step 3: Pull out common terms that exists in the radicand.
Remember that when a number appears under the square root sign, one of the numbers can be brought out front and the other one is canceled out.
Step 4: Use the identity that 
Example Question #1 : The Complex Number System
Express 
A pure imaginary number is expressed as 
Example Question #2 : The Complex Number System
Express 
A pure imaginary number is expressed as 
Example Question #3 : The Complex Number System
Simplify:
Example Question #4 : The Complex Number System
Simplify:
Example Question #5 : The Complex Number System
Simplify:
Example Question #1 : The Complex Number System
Simplify
The powers of 
This pattern continues for every successive four power of 
Example Question #6 : The Complex Number System
Simplify:
The powers of 
This pattern continues for every successive four power of 
Example Question #9 : The Complex Number System
Simplify:
The powers of 
This pattern continues for every successive four power of 
Example Question #10 : The Complex Number System
Simplify:
The powers of 
This pattern continues for every successive four power of 
To simplify 
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