Alerts Wishlist Cart

If z = e^(iπ/4), find the value of z^8.

Practice Questions

Q1
If z = e^(iπ/4), find the value of z^8.
  1. 1
  2. 0
  3. -1
  4. i

Questions & Step-by-Step Solutions

If z = e^(iπ/4), find the value of z^8.
Correct Answer: 1
  • Step 1: Start with the given value of z, which is z = e^(iπ/4).
  • Step 2: To find z^8, we need to raise z to the power of 8. This means we calculate (e^(iπ/4))^8.
  • Step 3: When raising a power to another power, we multiply the exponents. So, (e^(iπ/4))^8 = e^(i(π/4) * 8).
  • Step 4: Calculate the exponent: (π/4) * 8 = 2π. So now we have e^(i2π).
  • Step 5: Recall that e^(i2π) is a well-known result in complex numbers, which equals 1.
  • Step 6: Therefore, z^8 = 1.
No concepts available.
Biology (School & UG)
Biology (School & UG)
Chemistry (School & UG)
Chemistry (School & UG)
Civil Engineering
Civil Engineering
Commerce & Accountancy
Commerce & Accountancy
Computer Science & IT
Computer Science & IT
Current Affairs & GK
Current Affairs & GK
Data Structures & Algorithms
Data Structures & Algorithms
eBooks
eBooks
Electrical & Electronics Engineering
Electrical & Electronics Engineering
English (School)
English (School)
General Aptitude
General Aptitude
General Knowledge
General Knowledge
General Knowledge & Current Affairs
General Knowledge & Current Affairs
Languages & Literature
Languages & Literature
Law & Legal Studies
Law & Legal Studies
Major Competitive Exams
Major Competitive Exams
Mathematics (School)
Mathematics (School)
Mechanical Engineering
Mechanical Engineering
Medical Science
Medical Science
Physics (School & Undergraduate)
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Quantitative Aptitude & Reasoning
Social Science (School)
Social Science (School)
Technical
Technical
Verbal and Reasoning
Verbal and Reasoning
Vocational & Skill Development
Vocational & Skill Development
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely