FM - Core Pure 1 - 1) Complex numbers

Question 1

Results of i¹ i² i³ i⁴

Answer 1

• i¹ → √-1
• i² → -1
• i³ → -i
• i⁴ → 1
  (and the cycle continues)

Question 2

Complex conjugate of z = a + bi and how they appear together

Answer 2

• z* = a - bi
• Appear as a pair of non-real, complex roots

Question 3

Equations of a quadratic which has roots α and ß

Answer 3

• (z - α)(z - ß)
• z² - (α + ß)z + αß = 0

Question 4

Possible roots of a cubic equation

Answer 4

• Three real roots
• One real root and a pair of complex conjugate roots

Question 5

Possible roots of a quartic equation

Answer 5

• Four real roots
• Two real roots and a pair of complex conjugate roots
• Two pairs of complex conjugate roots