Download Name: TP: ____ CRS NCP 605 – Multiply two complex numbers

CW#28H: Multiply Complex Numbers
Honors Geometry
Name: _____________________________ TP: ____
CRS
Objectives
NCP 605 – Multiply two complex numbers
5.11 Multiply two complex numbers
5.12 Multiply two binomials that include complex numbers
LET’S REMEMBER THAT:
In the set of real numbers, negative numbers do not have square roots. A new kind of number, called
___________________ was invented so that negative numbers would have a square root. These numbers start
with the number _______, which equals ___________.
Complex numbers include both ____________ and _______________ numbers.
Complex numbers consist of all sums a+bi where a and b are real numbers and i is imaginary. For
example, 5+6i is a complex number where 5 is the __________ part and 6i is the _________________ part.
Today we are going to multiply two complex numbers.
When performing any operation, the variable i behaves as any variable would.
Example 1:
3i(2i + 7)
Example 2:
3i•6i
Example 3:
i•2i •9
i is very unique and when we begin to raise i to different powers, we begin to see a ___________________.
i1 =
(-1 )
=
i
i2 =
i•i
=
-1 • -1
i3 =
i•i•i
=
=
i4 =
=
=
i5 =
=
=
i6 =
=
=
i7 =
=
=
i8 =
=
=
=
PUSH IT TO THE LIMIT.
What we see is a _______________ of four numbers: _______, _______, _______, and _______.
Since i4 = 1, when we see i raised to a very large power, we should always rewrite it to a power of ________.
We can do this in two ways.
1. By using rules of exponents.
2. By using long division.
Example 4: i6
Example 5: i10
Example 6: i17
Now let’s put it all together.
Step 1: Group and multiply all ________________ numbers.
Step 2: Group all ___________________ numbers. Remember the product rule! i3i4=i12
Step 3: Divide the imaginary number exponent by 4, and substitute in the number 1. BECAUSE:

i2= -1. Therefore, i2∙i2=
_____________ = _______.
Step 4: After dividing by 4, the remainder is the resulting exponent of the imaginary number.
Step 5: If possible, simplify the remaining imaginary number.

For example, if left with i3, simplify to: ___________ = _________
Step 6: If multiplying two ________________, FOIL! And follow steps 2 through 5.
Step 7: Write your answer in the form __________________.
Example 7:
(3i)(-4i)(- i) =
Example 8:
i3 • 3i4 • -6i
Example 10: Find values of x and y
to make each equation true.
3 x  2iy  6  10i
PUSH IT TO THE LIMIT.
Example 9: (3 + 2i)(4 – 5i)
Name: _____________________________ TP: ____
CW#28H: Multiply Complex Numbers
Honors Geometry
1) 5i(i + 6)
2) 8i•4i
3) i•4i •7
4) i9
5) i21
6) i40
7) 2i2 • -i3 • -6i
8) i5 • i4
9) -8i2 • 3i2 • -6i
10) 5i • -10i2 • i4
11) (-2 - 6i)(-8 - 4i )
12) (-4 + 7i)(10 - 4i)
13) 8i (6 - 2i)
14) -8i – 4(i + 3i²)
15) (4 -2i) (3+ 5i)
16) The product of two real
numbers …
17) The product of two complex
numbers...
18) The product of two pure
imaginary numbers…
A. will be real.
B. will be complex.
C. will be pure imaginary.
D. could be any of the above.
A. will be real.
B. will be complex.
C. will be pure imaginary.
D. could be any of the above.
A. will be real.
B. will be complex.
C. will be pure imaginary.
D. could be any of the above.
PUSH IT TO THE LIMIT.
19) Find values of x and y to make each equation true.
20) Find values of x and y to make each equation true.
3 x  2iy  6  10i
4 x  iy  8  7i
21) Simplify:
22) Simply:
(2  i)(3  2i)(1  4i)
(1  3i)( 2  2i)(1  2i)
24) Multiply and simplify: (-3 + 4i)2.
23)
A.
B.
C.
D.
-9 + 16i
-7 – 24i
9 – 16i
6 + 9i
The voltage E, current I, and impedance Z in a circuit are related by E  I  Z . Find the voltage (in volts) in
each of the following circuits given the current and impedance.
25) I  1  3 j amps, Z  7  5 j ohms
26) I  2  7 j amps, Z  4  3 j ohms
27) Which of the following is equivalent
to i33?
A.
B.
C.
D.
1
i
-1
-i
28) Multiply and simplify: (2 – 3i)4
A.
B.
C.
D.
8 – 12i
16 – 81i
-58 + 112i
-119 + 120i
PUSH IT TO THE LIMIT.