Patterns
i0=
1
1+3i+2i
1+5i
treat the imaginary number as you would a variable.
only add the -3 and 2
-3+12i-2i=
-3+10i
Combine like terms
i goes at end
(3i)(8i)=
-24
(3x8)=24 (ixi)=i2=-1
(24)(-1)
To find this, you keep the real part the same and change the sign of the imaginary part bi to −bi
How do you find the conjugate of an expression?
i1=
i
9+14i+2i=
9+16i
Treat i like a variable
only add like terms.
-8+22i-44i=
-8-22i
Combine like terms
i goes at end
(2+4i)(3+5i)=
-14+22i
Foil: 6+10i+12i+20i2
Combine like terms: 6+22i+20i2
Simplify i2: 6+22i-20
Combine again:
1. Identify the conjugate of the denominator
2. Multiply the numerator and the denominator by the conjugate of the denominator
3. Simplify the resulting expression.
What the steps to dividing imaginary numbers?
i2=
-1
(15+2i)+(16+-1i)=
31+i
(15+2i)+(16+-1i) can be rewritten as 15+16+2i+-1i
combine like terms
(15+2i)-(13+i)=
2+i
Change to: 15-13+2i-i
Combine like terms
(2-4i)(3-5i)=
-14-22i
Foil:6-10i-12i+20i2
Simplify: 6-22i-20
Combine like terms:
(1+2i)/(3+4i)
11/5 - (2/5)i
i3=
-i
(2-12i)+(-4-12i)=
-2-24i
rewrite as: -12i+-12i+2+-4
combine like terms
(15+12i)-(-13+13i)=
28-i
change to: 15+13+12i-13i
Combine like terms
(6+12i)(2-4i)=
60
Foil: 12-24i+24i-48i2
Simplify:12+48
Combine like terms:
Find the conjugate of the denominator:
(12-21i)/(-6-9i)
-6+9i
Switch middle sign.
i40=
1
40/4=10 with a remainder of 0
This means i40= i0=1
(-322-16i)+(55-12i)=
-267-28i
rewrite as -16i+-12i+-322+55
Combine like terms
(144-154i)-(-122+43i)=
266-165i
change to: 144+122+-154i-43i
combine like terms
2i(12+4i)(6+8i)=
-240+80i
multiply 2i: (24i+8i2)(6+8i)
simplify: (8i+24i)(6+8i)
foil: -48-64i+144i+192i2
simplify: -48+80i-192
Combine like terms:
Solve: (12-21i)/(-6-9i)
1+2i
Multiply by conjugate over itself:
(12-21i)(-6+9i)/(-6-9i)(-6+9i)
Foil:
(-72+108i+126i+189i2)/(36-54i+54i-81i2)
Simplify:
(-72+234i+189)/(36+81)
Combine like Terms:
(117+234i)/(117)
Divide: