Complex Numbers and Their Operations
Math ⇒ Number and Operations
Complex Numbers and Their Operations starts at 11 and continues till grade 12.
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See sample questions for grade 12
Divide (6 + 8i) by (2 - 2i) and express the answer in the form a + bi.
Express 8(cos 60° + i sin 60°) in the form a + bi.
Express the product (2 + 3i)(1 - 4i) in the form a + bi.
Express the quotient (7 + 24i) / (4 - 3i) in the form a + bi.
If z = 1 + i, what is z10?
If z = 2 - 5i, find z2.
If z = 2 + 2i, what is the modulus squared of z?
If z = 3 - 4i, what is 1/z in the form a + bi?
Which of the following is NOT a complex number?
(1) 2 + 3i
(2) 0
(3) 5
(4) None of the above
Which of the following is the correct geometric representation of multiplication by i in the complex plane?
(1) Rotation by 90° counterclockwise
(2) Reflection about the real axis
(3) Dilation by a factor of i
(4) Translation by i units
Which of the following is the correct value of i15?
(1) i
(2) -i
(3) 1
(4) -1
Which of the following is the multiplicative inverse of 1 + i?
(1) 1 - i
(2) (1 - i)/2
(3) (1 + i)/2
(4) -1 - i
Fill in the blank: The imaginary part of the complex number -6 + 11i is _______.
Fill in the blank: The imaginary unit i is defined as i = _______.
Fill in the blank: The real part of the complex number 9 - 4i is _______.
Fill in the blank: The set of all complex numbers is denoted by _______.
True or False: The argument of a positive real number is 0.
True or False: The complex conjugate of a real number is the number itself.
True or False: The product of a complex number and its conjugate is always a real number.
True or False: The set of complex numbers is closed under addition, subtraction, multiplication, and division (except by zero).
