Chp 2: Complex Number

Question 1

Complex number consists of …

Answer 1

Real part + imaginary part

Question 2

General/cartesian/rectangular form of complex no

Answer 2

x + iy

Question 3

Polar form of complex no

Answer 3

Z=r (cos theta + i sin theta)

Z= r L theta

Question 4

r L - theta

Answer 4

r (upside down L) theta

Question 5

X in polar form

Answer 5

Z1Z2 = r1r2 L theta1 + theta2

Question 6

/ in polar form

Answer 6

Z1/Z2 = Z1/Z2 L theta1 - theta2

Question 7

De moivre’s theorem of r^n ( cos theta + i sin theta)^n

Answer 7

r^n (cos ntheta + i sin ntheta)

Question 8

De moivre’s theorem of nth root term

Answer 8

Z^1/n = r^1/n ( cos 2kpi+ theta/ n + i sin 2kpi + theta / n )

Question 9

Exponential form

Answer 9

Z = re^ itheta (theta is in radians)

e^itheta = ( cos theta + i sin theta)

e^-itheta = ( cos theta - i sin theta)

Question 10

Sum of Z and Its conjugate

Answer 10

2x

Question 11

Subtraction of Z By Its conjugate

Answer 11

2y

Question 12

Z^2

Answer 12

a^2 + 2iab - b^2

Question 13

Conjugate of Z^2

Answer 13

a^2 - 2iab - b^2

Question 14

Z x conjugate of Z

Answer 14

a^2 + b^2

Question 15

Z / conjugate of Z

Answer 15

a^2 + 2iab - b^2 / a^2 + b^2

Question 16

i

Answer 16

i (-1)^1/2

Question 17

i^2

Answer 17

-1

Question 18

i^3

Answer 18

-i

Question 19

i^4

Answer 19

1

Question 20

e^itheta + e^-itheta

Answer 20

2 cos theta —> can derive into hyperbolic

Question 21

e^itheta - e^-itheta

Answer 21

2 i sin theta —> can derive into hyperbolic