Complex Numbers Review
i = ?
√-1
Find the Quotient (2 + 3i)/(4 - 2i)
(1 + 8i)/10
i³ = ?
- √- 1 or just: - i
i² = ?
-1
simplify i⁴²
-1
i squared
-1 (negative 1 or minus 1)
Write the complex number in Standard Form (√-4)² - 7
-11
Find the sum √-4 + (-4 - √-4)
-4
Write the complex number in Standard Form √-9 - 5
-5 + 3i
i cubed
-i
simplify i²⁷
-i
i to the fourth
1
i⁴ = ?
1
simplify i⁸
1
Find the product. (2 - i)(4 + 3i)
11 + 2i
Find the product. (5 - 3i)²
16 - 30i
Find the product. 8i(4 - 3i)
24 + 32i
Write the complex number in Standard Form -3i² + i
3 +i
Write the complex number in Standard Form -√-12 + 3
3 -2i√3
Find the product. (3 - 5i)(3 + 5i)
34
Find the sum (3 - i) + (2 + 3i)
5 + 2i
Simplify 4i - (-3 + 5i) + (2 - 6i)
5 - 7i
Find the Quotient -5/2i
5i/2
What is a complex number?
A number that has both a real portion and an imaginary portion to it. Such as a + bi a is real but b is being multiplied by the imaginary unit and is thus imaginary
Rational Numbers
Can be expressed exactly as a ratio of two integers
Irrational Numbers
Cannot be expressed exactly as a ratio of two integers, but are real numbers
Real Numbers
Have points on the number line
Complex Numbers
Have the form a+bi, where a and b are real, and i=√ -1
Radicals
Involve square root, cube root, etc. of integers
If i is raised to any multiple of 4 such as: i⁸, i¹², i¹⁶, .....i⁴ⁿ then?
It still equals 1 just like i⁴
How are complex numbers multiplied?
Just like regular numbers and variables. Final answer however should not have any power of i higher than 1.
How are complex numbers divided?
Multiply the numerator and the denominator of the fraction by the conjugate of the denominator
Imaginary Numbers
Square roots of negative numbers. Have no points on the number line
Integers
Whole numbers and their opposites
When adding and subtracting complex numbers what is the rule?
You can only add/subtract reals numbers with real numbers and imaginary number with imaginary numbers.
i to the fifth
i
simplify i³⁷
i
i
the square root of negative 1 ie.√ -1