PRACTICE IN COMPLEX NUMBERS FOR SAT

Problem 1 :

For i = √-1, which of the following is equivalent to

(5 - 3i) - (-2 + 5i) ?

(a)  3 - 8i    (b)  3 + 2i     (c) 7 - 8i    (d)  7 + 2i

Solution

Problem 2 :

Given that i = √-1, which of the following is equal to i(i + 1) ?

(a)  i - 2    (b)  i - 1     (c) i + 1    (d)  0

Solution

Problem 3 :

i⁴ + 3i² + 2

Which of the following is equal to the expression above.

(a)  i    (b)  - 1     (c) 0     (d)  1

Solution

Problem 4 :

(6 +2i) (2 + 5i)

If the expression above is equivalent to a + ib, where a and b are constants. What is the value of a?

(a)  2    (b)  12     (c) 22     (d)  34

Solution

Problem 5 :

Which of the following is equal to 

3(i + 2) - 2(5 - 4i)?

(a)  16 - 5i    (b)  -4 + 7i     (c) -4 + 11i     (d)  16 + 11i

Solution

Problem 6 :

Which of the following equivalent to 3i(i + 2) - i(i - 1) ?

(a)  -4 + 7i    (b)  -2 + 7i     (c) -4 + 5i     (d)  -2 + 5i

Solution

Problem 7 :

Which of the following is equivalent to i⁹³ ?

(a)  -1    (b)  1     (c) -i     (d)  i

Solution

Problem 8 :

Which of the following complex number is equivalent to

(3 - i)² ?

(a)  8 - 6i    (b)  8 + 6i     (c) 10 - 6i     (d)  10 + 6i

Solution

Problem 9 :

(5 - 2i)(4 - 3i)

Which of the following is equal to the expression above ?

(a)  14 - 7i    (b)  14  - 23i     (c) 26 + 7i     (d)  26 - 23i

Solution

Problem 10 :

Which of the following is equal to 

(a)  -i    (b)  i     (c) 0     (d)  1

Solution

Problem 11 :

Which of the following is equal to 

(a)  -i    (b)  i     (c) (-5/4)i     (d)  (3/4) - (5/4)i

Solution

Problem 12 :

Which of the following complex number is equivalent to 

(2 - i)/(2 + i) ?

Solution