Complex Number

• 1) Complete the following i³ = ?

•   -1
•   -i
•   i
•   1

• 2) Complete the following i¹³⁵ = ?

•   -i
•   -1
•   1
•   i

• 3) Complete the following i¹⁹ = ?

•   -i
•   i
•   1
•   -1

• 4) Complete the following i⁻⁹⁹⁹ = ?

•   1
•   -1
•   i
•   -i

• 5) The real part of i is

•   1
•   5
•   3
•   0

• 6) What does e^iθ stands for ?

•   cosθ + i sinθ
•   sinθ – i cosθ
•   cosθ - i sinθ
•   i sinθ + cosθ

• 7) Compute the given number √-144 =?

•   12i
•   -12i
•   -13i
•   13i

• 8) Compute the given number √-169 = ?

•   i - 13
•   13/i
•   13i
•   i + 13

• 9) Compute the given √-4 × √-9/4

•   -2
•   -4
•   -3
•   -1

• 10) If z = 2 – iy and z = x + 3i then find x and y.

•   -4,-4
•   -2, 3
•   2,-3
•   -3, 2

• 11) Find the real values of x and y if (3x – 7) + 2iy = - 5y + (5 +x)i

•   x = -2 , y = -2
•   x = 2 , y = -2
•   x = -1 , y = 2
•   x = 1 , y = 2

• 12) Find the values of x and y if (x + iy ) (2 – 3i) = 4 + i

•   (15/17) , (15/13)
•   (15 + 13) , (14 - 13)
•   (15/13) , (14/13)
•   (15 - 17) , (15 + 13)

• 13) Find the values of x and y if (1 – i) x + (1 + i) y = 1 – 3i

•   -1, 2
•   -2, 1
•   1, 2
•   -1,-2

• 14) Find the value for the relation.

•   z1
•   ² -
•   5(
•   z2

• 15) Find real values of x and y(1 + i)y² + (6 + i) = (2 + i)x

•   3 , ±6
•   4 , ±7
•   7 , ±3
•   5 , ±2

• 16) Solve the equations 4x² + 9 = 0 by factorization method.

•   -(4/2)i
•   (3/2)i
•   (4/2)i
•   -(3/2)i

• 17) Solve the equation x² - 4x + 13 = 0 by factorization method.

•   5 - 2i , -4 + 3i
•   2 + 3i , 2 – 3i
•   -2 - 3i , 4 – 3i
•   – 3 - 2i, 3 + 2i

• 18) Solve the equation x² - 5ix – 6 = 0 by factorization method.

•   3i, - 2i
•   7i, -8i
•   3i, 2i
•   5i, 4i

• 19) Solve the equation x² + 4ix -4 =0 by factorization method.

•   2i, 2i
•   4i, 4i
•   -2i, -2i
•   -4i + 4i

• 20) Solve the equation 3x² + 7ix + 6 =0 by factorization method.

•   8i, (3/4)i
•   3i, (2/3)i
•   4i, (2/3)i
•   -3i, (2/3)i

• 21) Solve the equation x² + 1 = 0 by factorization method.

•   ±2
•   ±4
•   ±1
•   ±3

• 22) Solve the equation 9x² + 4 = 0 by factorization method.

•   ± i(5/3)
•   ± i(3/2)
•   ± i(2/3)
•   ± i(9/3)

• 23) Solve the equation 2x² - 4x + 3 = 0 by formula method.

•   x = (-1 ± (1 / √2)i)
•   x = (2 ± (1 / √5)i)
•   x = (7 ± (6 / √9)i)
•   x = (1 ± (1 / √2)i)

• 24) Solve the equation 27x² - 10x + 1 = 0 by formula method.

•   x = (9 ± i√3)/25
•   x = (-5 ± i√3)/27
•   x = (5 ± i√2)/27
•   x = -(5 ± i√2)/24

• 25) Solve the equation - x² + x - 2 = 0 by formula method.

•   x = 1 ± i √5/-2
•   x = -1 ± i √7/-2
•   x = 1 ± i √9/-2
•   x = -1 ± i √7/2

• 26) Solve the equation x² - 2x + (3/2) = 0 by formula method.

•   2 ± (i/√9)
•   2 ± (i/√5)
•   ±(i /√2)
•   1 ± (i/√3)

• 27) Solve the equation 2x² + 3ix + 2 = 0 by formula method.

•   x = i / 4 or -4i
•   x = i / 8 or -8i
•   x = i / 2 or -2i
•   x = i / 3 or -2i

• 28) Solve the equation i x² - x + 12i = 0 by formula method.

•   x = (4/i) or (- 3i)
•   x = (-4/i) or (3i)
•   x = (5/i) or (- 3i)
•   x = (6/i) or (-3i)

• 29) Solve the equation x² + x + (1 /√2) = 0

•   x = -3 ± i√(3√2 -1)/6
•   x = 2 ± i√(2√3 - 1)/4
•   x = -2 ± i√(2√3 - 1)/3
•   x = -1 ± i√(2√2 -1)/2

• 30) Solve the equation x² - 8x + 24 = 0 by completing the square method.

•   x = - 4 ± 2√2i
•   x = 3 ± 3√2i
•   x = 5 ± 5√2i
•   x = 4 ± 2√2i