Unit 2 Complex Numbers Study Guide

number pairs of the form a + bi and a - bi & example

complex conjugate 3i^2, -3i^2

the set of real and imaginary numbers & example

complex number 3 + 4i, 2, 6i

Simplify the expression: -10-i ------- -2i

i/-2i - 5i

any number of the form a + bi where a and b are real numbers and b ≠ 0 & example

imaginary number 3+2i, 6-2i

an imaginary number of the form a + bi where a = 0 & example

pure imaginary number 2i, 1/2i, -3i

the symbol √ is called...

radical, square root sign

the number inside the radical sign & example

radicand √2

Solve for x & y: 2x+8+5yi=6x-4

x=3 y=0

Solve for x & y: 5+x-8i=10+2yi

x=5 y=-4

Give a quadratic equation with the given root: x=6i

y=x^2+36

Give a quadratic equation with the given root: x=4-2i

y=x^2-8x+20

find the absolute value of each complex number: |-2+5i| =

√-2^2+5^2 √4+25 √29

find the absolute value of each complex number: |-6i| =

√-6^2 √36 √6

find the absolute value of each complex number: |4-4i| =

√4^2 + 4^2 √16+16 √32 √4√2

find the absolute value of each complex number: |5+3i| =

√5^2 + 3^2 √25+9 √34

Simplify the expression: (3+4i) + (-2-5i)

-1-1i

Simplify the rational expression: (-7+5i√3)(2+i√3)

-29+3i√3

Simplify the expression: (-1+6i) - (8-3i)

-9+9i

Simplify the expression: (2+2i)(8-i)

16-2i+16i-2i^2 16-14i+2 18-14i

Simplify the expression: 2-2i ----- 5+3i

2/17 - 8/17 i

Simplify the rational expression: 4+√3 -------- 2+√3

5-2√3

Simplify the expression: (3+i)(3-i)

9-3i+3i-i^2 9+1 10