Questions with answers on
complex numbers. In what follows i denotes the imaginary unit defined by i = sqrt ( -1 ).

**Question 1:**Add and express in the form of a complex number a + b i.

(2 + 3i) + (-4 + 5i) - (9 - 3i) / 3

**Question 2:**Multiply and express in the form of a complex number a + b i.

(-5 + 3i)(- 4 + 8i)

**Question 3:**Divide and express in the form of a complex number a + b i.

(-1 - 2i) / (- 4 + 3i)

**Question 4:**Find the complex conjugate to.

1 + 8i

**Question 5:**Express in the form of a complex number a + b i.

(-5 - i)(- 7 + 8i) / (2 - 4i)

**Question 6:**Express in the form of a complex number a + b i.

- (7 - i)(- 4 - 2i)(2 - i)

**Question 7:**Express in the form of a complex number a + b i.

i / (1 - i)

**Question 8:**Solve for x and y where x and y are real numbers.

2 y + i x = 4 + x - i

**Question 9:**Find a and b, where a and b are real numbers so that

a + i b = (2 - i)^{2}

**Question 10:**Find the complex conjugate to

- 3 i

__Solution to Above Questions.__

**question 1:** -5 + 9 i

**question 2:** -4 - 52 i

**question 3:** -2 / 25 + (11 / 25) i

**question 4:** 1 - 8 i

**question 5:** 109 / 10 + (53 / 10) i

**question 6:** 70 - 10 i

**question 7:** -1 / 2 + i / 2

**question 8:** x = -1 , y = 3 / 2

**question 9:** a = 3 , b = -4

**question 10:** 3 i

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