Complex Numbers Flashcards
A complex number is a number in the form
x + yi
x is a real number called the
real part
y in a complex number is the
imaginary part
i = √-1 is called an
imaginary number
3 + 5i
real part = ?, imaginary part = ?
real part = 3, imaginary part = 5i
In 4i, determine the real part and imaginary part.
real part = 0, imaginary part = 4i
Determine the real and imaginary part of 7.
real part = 7, imaginary part = 0
i⁰ =
1
i¹ is equal to
i
i² =
-1
i³ =
-i
i⁴ =
1
Simplify: i²⁰¹⁷ + 2i²⁰¹⁸ - 3i²⁰²⁰
-5 + i
Determine the values of x and y in the complex number 2( x + iy ) = 6 - i3.
x = 3, y = - 3/2
Operations of Complex Numbers in Algebraic Form
( 5 + 2i ) - ( 4 - 3i) = ?
1 + 5i
Operations of Complex Numbers in Algebraic Form
( 3 + 2i ) ( 2 - 5i) = ?
16 - 11i
Operations of Complex Numbers in Algebraic Form
( 4 - 2i )/( 3 + 2i ) = ?
8/13 - 14i/13
Complex Number in Trigonometric Form
x + iy = ?
r( cosθ + isinθ ) or rcisθ
Complex Number in Polar Form
x + iy = ?
r∠θ
Absolute value or modulus of the complex number
r = √(x² +y²)
Argument or amplitude of the complex number
θ = arctan y/x
Express 3 + 4i in trigonometric form.
5( cos53.13° + isin53.13° )
Express 2( cos30° + isin30° ) in algebraic/rectangular form.
√3 + i
Multiply ( 3cis20° ) ( 2cis40° ) in trigonometric form.
6 ( cos60° + isin60°)
Divide 6angle60°/2angle20°.
3angle40°
Evaluate ( 1 + i )⁵ and express the answer in x + yi.
-4( 1 + i )
Find the 3 cube roots of -1 + i√3.
1st root = cube root of 2 angle 40°
2nd root = cube root of 2 angle 160°
3rd root = cube root of 2 angle 280° or cube root of 2 angle( -80° )
What is the product of the complex numbers 3 - 4i and 8e^i53.13°?
40
Evaluate ln( 3 + 4i ) in rectangular form.
1.609 + 0.927i
Complex Number in Exponential Form
re^iθ
