iClock
How to Use the iClock
The beautifully illustrated mathematical concept of solves powers of i. The inside of the clock is used for counting. The outside correlates the mathematical value for the amount of times you counted around the clock.
Let’s say the math problem involved a number greater than ten. It makes no sense to waste time and physical energy rotating around the clock. Instead, divide the exponent by four and use the remainder of that number to count around the clock.
For example:
i145,122 = 1
Why? The powered 145122/4 has a remainder of 2. Therefore, using the iClock, count around the clock for the value of i once powered.
Note: If there is a co-efficient before i, the result of that number squared will be multiplied by that number.
Addition of Complex Numbers
(9 + 13i) + (6 + 7i)
9 + 13i + 6 + 7i
15 + 13i + 7i
15 + 13i + 7i
15 + 20i
Step 1: Since every number on here has the same mathematics sign, the parenthesis can be dropped.
Step 2: From there combine like terms.
Step 2.1: For mine I first combined the numbers that with out i.
Step 2.2: Next I combined the like terms with i.
Step 3: You now have a simplified expression.
SIDE NOTE - DON'T TRY TO COMBINE NUMBERS WITH i IF THEY DON'T HAVE i ONLY COMBINE LIKE TERMS!
Step 1: Since every number on here has the same mathematics sign, the parenthesis can be dropped.
Step 2: From there combine like terms.
Step 2.1: For mine I first combined the numbers that with out i.
Step 2.2: Next I combined the like terms with i.
Step 3: You now have a simplified expression.
SIDE NOTE - DON'T TRY TO COMBINE NUMBERS WITH i IF THEY DON'T HAVE i ONLY COMBINE LIKE TERMS!
Subtraction of Complex Numbers
(32 + 27i) – (-44 – 31i)32 + 27i + 44 + 31i
76 + 58i
Step 1: First you want to use the minus sign between the two sets of parenthesis'.
Step 1.1: You use it by making everything in the parenthesis to the right of it negative. For instance I had a negative 44 minus a 31i. So then it changed to a POSITIVE 44 PLUS 31i.
Step 2: From there combine like terms.
Step 2.1: For mine I first combined the numbers that with out i.
Step 2.2: Next I combined the like terms with i.
Step 3: You now have a simplified expression.
SIDE NOTE - DON'T TRY TO COMBINE NUMBERS WITH i IF THEY DON'T HAVE i ONLY COMBINE LIKE TERMS!
Step 1: First you want to use the minus sign between the two sets of parenthesis'.
Step 1.1: You use it by making everything in the parenthesis to the right of it negative. For instance I had a negative 44 minus a 31i. So then it changed to a POSITIVE 44 PLUS 31i.
Step 2: From there combine like terms.
Step 2.1: For mine I first combined the numbers that with out i.
Step 2.2: Next I combined the like terms with i.
Step 3: You now have a simplified expression.
SIDE NOTE - DON'T TRY TO COMBINE NUMBERS WITH i IF THEY DON'T HAVE i ONLY COMBINE LIKE TERMS!
Note: The properties of addition and subtraction allow like terms to be combined to simplify a problem.
Division of complex numbers with radicals
To divide radicals with complex numbers, one must remember the quotient property:
Let's simplify the problem
Step 1: Using the quotient property, separate the numerator and denominator by two separate radicals.
Step 2: Simplify.
Multiplying complex numbers
Let's do the problem
(2+6i)(5+8i)
Step 1: FOIL the two sets.
Step 2: Combine like terms.
Division of complex numbers with radicals
To divide radicals with complex numbers, one must remember the quotient property:
Let's simplify the problem
Step 1: Using the quotient property, separate the numerator and denominator by two separate radicals.
Step 2: Simplify.
Multiplying complex numbers
Let's do the problem
(2+6i)(5+8i)
Step 1: FOIL the two sets.
Step 2: Combine like terms.
(2+6i)(5+8i)
10+16i+30i+48i^2
10+46i-48
-38+46i
