Complex Numbers

Question 1

i=

Answer 1

√-1

Question 2

i squared

Answer 2

-1

Question 3

Addition of complex numbers

( a + bi) + (c + di) =

Answer 3

( a + bi) + (c + di) = (a+c) +(b+d) i

Question 4

Subtraction of complex numbers

( a + bi) - (c + di) =

Answer 4

(a-c) +(b-d) i

Question 5

Multiplication of complex numbers

( a + bi) (c + di) =

Answer 5

(ac-bd) + (ad+bc) i

Question 6

What is the conjugate of x + iy

Answer 6

x -iy

Question 7

Division of complex numbers

( a + bi) /(c + di) =

Answer 7

( a + bi) /(c + di) by (c -di)/ (c -di)

Question 8

Modulus, length, magnitude of z= x+ iy is

Answer 8

√x² + y²

Question 9

Argument of Z= x+ iy for each quadrant

Answer 9

1st quad: tan inverse (y/x)
2nd quad: tan inverse (y/x) + pi
3rd quad: tan inverse (y/x) -pi
4th quad: tan inverse (y/x)

Question 10

Complex number algebraic form

Answer 10

Z= x + iy

Question 11

Complex number polar / trigonometric form

Answer 11

Z = r (cosθ + isinθ)

Question 12

Complex number exponential form

Answer 12

Z= re ^(iθ)
where e^(iθ)=cosθ+sinθ

Question 13

square root of a complex number procedure

Answer 13

√x+iy = x+iy
square both sides
then equate real and imaginary parts

Question 14

quadratic equation in terms of z using roots

Answer 14

z²-(sum of roots)z +products of roots