High School Common Core Mathematics

Front 1

To represent complex numbers a+bi geometrically, the coordinate system is used with the horizontal axis representing the (real, imaginary) part of the complex number and the vertical axis representing the (real, imaginary) part of the complex number.

Back 1

To represent complex numbers a+bi geometrically, the coordinate system is used with the horizontal axis representing the real part of the complex number and the vertical axis representing the imaginary part of the complex number.

Front 2

What is the rectangular form of a complex number? Give an example of when rectangular form is used.

Back 2

The rectangluar form is where the complex number is denoted by its respective horizontal and veritcal components, where the horizontal component is the real part of the complex number and the vertical component is the imaginary poart of the complex number. The rectangular form is used to describe for far left/right and how far up/down and is written as a sum. An example of rectangular form would be saying the distance is 4+4i for 4 units right and 4 units up.

Front 3

What is the polar form of a complex number? Give an example of when polar form is used.

Back 3

The polar form is where a complex number is denoted by the length (absolute value) and the angle of its vector. An example would be saying the vector for New York to San Diego is 2400 miles, southwest.

Front 4

Why do the rectangular and polar forms of a given complex number represent the same number?

Back 4

The polar form of a complex number can be viewed as the hypotenuse of a right triangle where the rectangular form of the same complex number is the legs of that right triangle. The starting point and ending point are the same for both polar and rectangular forms, so they represent the same number.

Front 5

Show 2-3i on the complex plane.

Back 5

Front 6

Add 3+2i and 1+3i geometrically on the complex plane.

Back 6

Front 7

Subtract 5+1i - 2+5i geometrically on the complex plane.

Back 7