Information
You have already completed the quiz before. Hence you can not start it again.
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
Question 1 of 6
Incorrect
Loaded : 0%
Progress : 0%
0:00
Imaginary numbers has the property i 2 = - 1
To solve 6 1 + i 6 1 + i 1 - i
6 1 + i Multiply the numerator and the denominator by the conjugate 1 - i
= 6 1 + i × 1 - i 1 - i
= 6 - 6 i 1 - i + i - i 2 Combine like terms - i i
= 6 - 6 i 1 - i 2 Remember that i 2 = - 1
= 6 - 6 i 1 - ( - 1 ) Simplify
= 6 - 6 i 2 Divide both terms in the numerator by 2
= 3 - 3 i
Question 2 of 6
Incorrect
Loaded : 0%
Progress : 0%
0:00
Imaginary numbers has the property i 2 = - 1
To solve - 7 - 3 i 4 i i
- 7 - 3 i 4 i Multiply the numerator and the denominator by i
= - 7 - 3 i 4 i × i i
= - 7 i - 3 i 2 4 i 2 Remember that i 2 = - 1
= - 7 i - 3 ( - 1 ) 4 ( - 1 ) Simplify
= - 7 i + 3 - 4 Divide both terms in the numerator by - 4
= 7 4 i - 3 4 Reverse the order of the terms. The term with the i
= - 3 4 + 7 4 i
Question 3 of 6
Incorrect
Loaded : 0%
Progress : 0%
0:00
Imaginary numbers has the property i 2 = - 1
To solve i 1 - 3 i i 1 - 3 i 1 + 3 i
i 1 - 3 i Multiply the numerator and the denominator by the conjugate 1 + 3 i
= i 1 - 3 i × 1 + 3 i 1 + 3 i
= i + 3 i 2 1 2 – ( 3 i ) 2 Take the square of ( 3 i ) 2
= i + 3 i 2 1 – 9 i 2 Remember that i 2 = - 1
= i - 3 1 + 9 Simplify
= i 10 - 3 10 Divide both terms in the numerator by 10
= - 3 10 + i 10 Rearrange.
Question 4 of 6
Incorrect
Loaded : 0%
Progress : 0%
0:00
Imaginary numbers has the property i 2 = - 1
To solve - 7 - 2 i 5 i - 7 - 2 i 5 i i
- 7 - 2 i 5 i Multiply the numerator and the denominator by the conjugate i
= - 7 - 2 i 5 i × i i
= - 7 i - 2 i 2 5 i 2 Remember that i 2 = - 1
= - 7 i + 2 - 5 Divide both terms in the numerator by - 5
= - 7 i - 5 + 2 - 5 Rearrange.
= 2 - 5 – 7 i - 5 Simplify.
= - 2 5 + 7 i 5
Question 5 of 6
Incorrect
Loaded : 0%
Progress : 0%
0:00
Imaginary numbers has the property i 2 = - 1
To solve 5 - 9 i 1 + i 5 - 9 i 1 + i 1 - i
5 - 9 i 1 + i Multiply the numerator and the denominator by the conjugate 1 - i
= 5 - 5 i - 9 i + 9 i 2 1 2 - i 2 Remember that i 2 = - 1
= 5 - 5 i - 9 i - 9 1 + 1 Combine the terms with i
= 5 - 14 i - 9 1 + 1 Combine the real numbers.
= - 4 - 14 i 2 Divide both terms in the numerator by 2
= - 4 2 - 14 i 2 Simplify.
= - 2 - 7 i
Question 6 of 6
Incorrect
Loaded : 0%
Progress : 0%
0:00
Imaginary numbers has the property i 2 = - 1
To solve 2 + 3 i 3 + 2 i 2 + 3 i 3 + 2 i 3 - 2 i
2 + 3 i 3 + 2 i Multiply the numerator and the denominator by the conjugate 3 - 2 i
= `(2+3i)/(3+2i)timescolor(red)(3-2i)/color(red)(3-2i)
= 6 - 4 i + 9 i - 6 i 2 3 2 - ( 2 i ) 2 Take the square of ( 2 i ) 2 3 2
= 6 - 4 i + 9 i - 6 i 2 9 - 4 i 2 Remember that i 2 = - 1
= 6 - 4 i + 9 i + 6 9 + 4 Combine the terms with i
= 6 + 5 i + 6 9 + 4 Combine all real numbers.
= 12 + 5 i 13 Divide both terms in the numerator by 13
= 12 13 + 5 i 13
