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7. $\left[\left(\frac{1}{3}+i\frac{7}{3}\right)+\left(4+i\frac{1}{3}\right)\right]-\left(-\frac{4}{3}+i\right)$

= $\frac{1}{3}$ + $i\frac{7}{3}$ + 4 + $i\frac{1}{3}$ + $\frac{4}{3}$ – i

= $\left(\frac{1}{3}+4+\frac{4}{3}\right)+i\left(\frac{7}{3}+\frac{1}{3}-1\right)$

= $\frac{1+12+4}{3}$ + $i\frac{7+1-3}{3}$

= $\frac{17}{3}$ + $i\frac{5}{3}$

Best short-term courses after B.Com include:

• Certificate in Digital Marketing
• Certificate in Financial Modeling
• Certificate in Business Analytics
• Certificate in Banking
• GST Certification Course

54. Kindly go through the solution

Yes, pursuing MBA after B.Com is an excellent option. It offers diverse specializations such as Finance, Marketing, HR, and Operations, which can lead to high-paying managerial and leadership roles. MBA enhances your business acumen, strategic thinking, and decision-making skills, making you more competitive in the job market. Additionally, it provides networking opportunities with industry professionals and peers, which can be invaluable for career growth. 

Top hiring companies for B.Com graduates include:

• Accounting and Auditing Firms: Deloitte, KPMG, PwC, Ernst & Young
• IT and Consulting Firms: TCS, Infosys, Accenture, Wipro
• Banking and Financial Services: HDFC Bank, ICICI Bank, SBI, Goldman Sachs, JP Morgan
• Public Sector Undertakings: BHEL, ONGC, SAIL, RBI
• Corporate Sector: Reliance, Tata Group, Aditya Birla Group

6. $\left(\frac{1}{5}+i\frac{2}{5}\right)$ – $\left(4+i\frac{5}{2}\right)$

= $\frac{1}{5}$ + $i\frac{2}{5}$ – 4 – $i\frac{5}{2}$

= $\frac{1}{5}$ – 4 + i $\left(\frac{2}{5}-\frac{5}{2}\right)$

= $\frac{1-20}{5}$ + i $\left(\frac{4-25}{10}\right)$

= $\frac{-19}{5}$ + i $\left(\frac{-21}{10}\right)$

= $\frac{-19}{5}$ – i $\frac{21}{10}$

Follow these ways here to be able to download the UPCATET Hall Ticket.

1. Go to the official UPCATET portal
2. Fill in the registration number, preferred course and date of birth.
3. Click on the download and take a printout of the entry card.

No, it is not mandatory to pursue a professional course after B.Com. However, a professional course can help you enhance your career in terms of specialization, high pay, better recognition in the industry, and also given a competitive edge.

5. (1 – i) – (–1 + i6)

= 1 – I + 1 – i6

= 2 – 7i

Below are some of the best professional courses that can help students earn higher salary:

• Chartered Accountancy (CA)
• MBA (Top Institutions)
• Chartered Financial Analyst (CFA)
• Association of Chartered Certified Accountants (ACCA)

The UPCATET 2026 admit card will be out on the official website on May 27, 2026, tentatively. Candidates who wish to appear for the UPCATET 2026 Exam must download their Hall ticket from the official website.

4. 3 (7 + i7) + I (7 + i7)

= 21 + 21i + 7i + 7i²

= 21 + 28i + 7 (–1) [since i² = –1]

= 21 + 28i – 7

= 14 + 28i

The institute has not released its course wise data yet. However, NIRF Report for 2025 is out. According to the NIRF report 319 PG 2-year students were placed during Bharathidasan University placements. Refer to the table below to know more:

Note: The data provided above is taken from NIRF report 2025

MNLU Mumbai cutoff 2025 has been released for round 1. The cutoff was released for General AI category and PWD AI category candidates, for BA LLB (Hons). The last round closing rank for the same was 536 for the General AI category. For the PWD AI category candidates, the closing ranks for BA LLB (Hons) was 18972. 

BBA new session will be released on the official website of Gujarat Technological University. As per the past academic calendar, classes for this batch are going to start in June, 2026. 

1. (5i) $\left(\frac{-3}{5}i\right)$

= 5 $\left(-\frac{3}{5}\right)$ ×i²          [since i² = –1]

= –3 (–1)

= 3

So, (5i) $\left(-\frac{3}{5}i\right)$ = 3 + i0