Complex Numbers
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by Meg Cohrs
| 22 Questions
1
1
Given the general form of a complex number, a+bi, (1) what is considered the real part of the complex number and (2) what is considered the imaginary part?
2
1
Given 3+4i, (1) what is the real part and (2) what is the imaginary part of the complex number?
3
1
Given 5+34i, (1) what is the imaginary part and (2) what is the real part of the complex number?
4
1
Given 15+i, (1) what is the real part and (2) what is the imaginary part of the complex number?
5
1
i²=
1
-1
i
-i
6
1
i³=
1
-1
i
-i
7
1
i4=
1
-1
i
-i
8
1
i5=
1
-1
i
-i
9
1
Simplify 4i2+2i+13.
-4+2i+13
9+2i
17+2i
19i
10
1
Explain your process in simplifying the expression in Question 9.
11
1
Multiply (2+3i)(4+6i) and show the product in simpliest form.
18i2+24i+8
8+18i2
-10+24i
6+9i
12
1
Explain your process in multiplying and reducing in Question 11.
13
1
Multiply the two complex numbers (2-5i2)(7+3i) and show the product in simpliest form.
-11-29i
-5i-2i3
-5i+3i-5i2
14-15i3
14
1
The conjugate of 5+8i is 5+8i.
True
False
15
1
The conjugate of a complex number involves the same real and imaginary part but changes the sign between them.
True
False
16
1
These two complex numbers are conjugates: (3+8i) and (3-8i).
True
False
17
1
The conjugate of 1+6i is 6+1i.
True
False
18
1
The conjugate of 4+i is _______.
19
1
What is the modulus if z= 7+9i. (Reduce to the simplest form)
|z|= 4
|z|= 3+ √7
|z|= √130
|z|= √63
20
1
Explain what steps you went through in Question 19 to find the modulus.
21
1
Use what we know about conjugates to simplify the following: (1+4i)/(9-5i)
10+i
29
9i/8
(-11+41i)/106
22
1
Explain how you simplified the expression in Question 21.