NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations Ex 5.1
Page No 103:
Question 1:
Express the given complex number in the form a + ib:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4120/CHAPTER%205_html_25bac34e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4120/CHAPTER%205_html_25bac34e.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4120/CHAPTER%205_html_m453d1698.gif)
Question 2:
Express the given complex number in the form a + ib: i9 + i19
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4121/CHAPTER%205_html_m37a02bf8.gif)
Question 3:
Express the given complex number in the form a + ib: i–39
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4122/CHAPTER%205_html_6922ff49.gif)
Page No 104:
Question 4:
Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4123/CHAPTER%205_html_54dd0223.gif)
Question 5:
Express the given complex number in the form a + ib: (1 – i) – (–1 + i6)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4124/CHAPTER%205_html_m42293290.gif)
Question 6:
Express the given complex number in the form a + ib:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4125/CHAPTER%205_html_288d8c03.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4125/CHAPTER%205_html_288d8c03.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4125/CHAPTER%205_html_m748555c9.gif)
Question 7:
Express the given complex number in the form a + ib:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4126/CHAPTER%205_html_3d2ee134.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4126/CHAPTER%205_html_3d2ee134.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4126/CHAPTER%205_html_6df08649.gif)
Question 8:
Express the given complex number in the form a + ib: (1 – i)4
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4127/CHAPTER%205_html_m25255def.gif)
Question 9:
Express the given complex number in the form a + ib:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4128/CHAPTER%205_html_m36d4877.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4128/CHAPTER%205_html_m36d4877.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4128/CHAPTER%205_html_5df9f9b4.gif)
Question 10:
Express the given complex number in the form a + ib:![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4129/CHAPTER%205_html_7b467239.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4129/CHAPTER%205_html_7b467239.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4129/CHAPTER%205_html_20f700cf.gif)
Question 11:
Find the multiplicative inverse of the complex number 4 – 3i
Answer:
Let z = 4 – 3i
Then,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4130/CHAPTER%205_html_5a697659.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4130/CHAPTER%205_html_30db9220.gif)
Therefore, the multiplicative inverse of 4 – 3i is given by
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4130/CHAPTER%205_html_5da9ac7a.gif)
Question 12:
Find the multiplicative inverse of the complex number ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4131/CHAPTER%205_html_564ca923.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4131/CHAPTER%205_html_564ca923.gif)
Answer:
Let z = ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4131/CHAPTER%205_html_564ca923.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4131/CHAPTER%205_html_564ca923.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4131/CHAPTER%205_html_m3879102d.gif)
Therefore, the multiplicative inverse of
is given by
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4131/CHAPTER%205_html_564ca923.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4131/CHAPTER%205_html_m160dd3b6.gif)
Question 13:
Find the multiplicative inverse of the complex number –i
Answer:
Let z = –i
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4132/CHAPTER%205_html_61daf497.gif)
Therefore, the multiplicative inverse of –i is given by
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4132/CHAPTER%205_html_2cba18df.gif)
Question 14:
Express the following expression in the form of a + ib.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4133/CHAPTER%205_html_329119fc.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4133/CHAPTER%205_html_24b3687e.gif)