Free Pre-Calculus Complex Numbers Questions and Answers

Question 1

Evaluate (4 - 2i)*(1 - 5i)

Accepted Answer

-6 - 22i

Answer

-7/15 - 4i/15

Answer

-5 + 7i

Answer

-4 + 2i

Question 2

What is the value of the expression (x + yi)(x - yi) if (x + yi) / i = 7 + 9i, where x and y are real numbers?

Accepted Answer

130

Answer

-130

Answer

0

Answer

26i

Question 3

Find all complex numbers z that satisfy the equation z + 3z' = 5 - 6i, where z' is the complex conjugate of z.

Accepted Answer

z = 5/4 + 3i

Answer

z = 5/4 - 3i

Answer

z = 5 - 3i

Answer

z = 5 + 3i

Question 4

Define Complex number.

Accepted Answer

A number of the form a + bi, where a and b are real numbers.

Answer

A number with only a real part.

Answer

A number of the form a + i, where a is a real number.

Answer

A number with only an imaginary part.

Question 5

Explain the real and imaginary components of a complex number.

Accepted Answer

The real part is the constant term, and the imaginary part is the coefficient of i.

Answer

The real part is the integer part, and the imaginary part is the fractional part.

Answer

The real part is the coefficient of i, and the imaginary part is the constant term.

Answer

The real part is the whole number, and the imaginary part is the decimal part.

Question 6

What is a complex number's conjugate?

Accepted Answer

A number obtained by changing the sign of the imaginary part.

Answer

A number obtained by adding i to the real part.

Answer

A number obtained by changing the sign of the imaginary part and the real part.

Answer

A number obtained by subtracting i from the imaginary part.

Question 7

Determine the conjugate of 2 - i.

Accepted Answer

-2 - i

Answer

2 - i

Answer

-2 + i

Answer

2 + i

Question 8

Add together the numbers (2 + 3i) and (-4 + 5i).

Accepted Answer

-2 + 8i

Answer

-2 - 8i

Answer

6 - 8i

Answer

6 + 8i

Question 9

What is the standard form of 4 - 5i

Accepted Answer

4 + (-5)i

Answer

4 - 5i

Answer

4 + (5)i

Answer

4 - (-5)i

Question 10

What is the "unit" imaginary number?

Accepted Answer

√(−1)

Answer

−1

Answer

0

Answer

1