Mathematics Questions and Answers – Complex Numbers-2

«
»

This set of Mathematics Question Bank focuses on “Complex Numbers-2”.

1. z1=1+2i and z2=2+3i. Find z1z2.
a) 2+6i
b) -4+0i
c) -4+7i
d) 8+7i
View Answer

Answer: c
Explanation: z1z2 = (1+2i) (2+3i)
= 2 + 3i + 4i -6
= -4 + 7i.
advertisement

2. i2 =______________________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: b
Explanation: We know, i = \(\sqrt{-1}\)
=> i2 = -1.

3. i7 =______________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: d
Explanation: We know, i = \(\sqrt{-1}\)
=> i2 = -1 => i4 = 1.
So, i7 = i4.i3 = 1*i2*i = (-1)*i = -i.
Sanfoundry Certification Contest of the Month is Live. 100+ Subjects. Participate Now!
advertisement
advertisement

4. i241 =________________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: c
Explanation: We know, i = \(\sqrt{-1}\)
=> i2 = -1 => i4 = 1.
So, i241 = (i4)60 * i = 1 * i = i.

5. Square roots of -7 are____________
a) 7i and -7i
b) \(\sqrt{7}\) i
c) –\(\sqrt{7}\) i
d) \(\sqrt{7}\) i and –\(\sqrt{7}\) i
View Answer

Answer: d
Explanation: We know, i2 = -1.
-7 = 7(i2)
Square root of i2 is ±i so, square root of -7 are \(\sqrt{7}\)i and –\(\sqrt{7}\)i.
advertisement

6. (-i) (8+5i) =________________
a) 8+5i
b) -8-5i
c) -5-8i
d) 5-8i
View Answer

Answer: d
Explanation: (-i) (8+5i) = -8i – 5 i2
= -8i -5(-1) = 5-8i.

7. (2-i)3 =________________
a) 2-3i
b) 8-i
c) 2-11i
d) 2+11i
View Answer

Answer: c
Explanation: We know, (a-b)3 = a3-b3-3ab(a-b)
So, (2-i)3 = 23-(i)3-3(2)(i) (2-i)
= 8-(-i)-6i(2-i)
= 8+i-12i-6
= 2-11i.
advertisement

8. Is z*\(\bar{z}\) = |z|2?
a) True
b) False
View Answer

Answer: a
Explanation: Let z=a+ bi
=>\(\bar{z}\) = a-bi
So, z*\(\bar{z}\) = (a+bi) (a-bi) = a2-(bi)2 = a2-(b2) (-1) = a2+b2
|z|=\(\sqrt{a^2+b^2}\) => |z|2 = a2+b2
Hence, z*\(\bar{z}\) = |z|2.

9. Find multiplicative inverse of 3+5i.
a) 87+145i
b) 87-145i
c) 145-87i
d) 145+87i
View Answer

Answer: b
Explanation: We know, z*\(\bar{z}\) = |z|2.
(1/z) = \(\bar{z}\)|z|2
z-1=(3-5i) (32+52) = (3-5i) (29) = 87-145i.
advertisement

10. i-35 =___________________
a) 1
b) -1
c) i
d) -i
View Answer

Answer: c
Explanation: We know, i-35= 1/i35 = i/i36
= i/(i4)9 = i/1 = i.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

To practice Mathematics Question Bank, here is complete set of 1000+ Multiple Choice Questions and Answers.

advertisement
advertisement
Subscribe to our Newsletters (Subject-wise). Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

Youtube | Telegram | LinkedIn | Instagram | Facebook | Twitter | Pinterest
Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

Subscribe to his free Masterclasses at Youtube & technical discussions at Telegram SanfoundryClasses.