Complex Number Quiz 1

Question 1

Express the given complex number in the form $$a + ib: (8 – i2) – (–1 + i7)$$.

Accepted Answer

$$9 – i9$$

Answer

$$8 – i9$$

Answer

$$9 – i8$$

Answer

$$8 – i8$$

Question 2

Express the given complex number in the form $$a + ib: 2(6 + i6) + i(6 + i7)$$

Accepted Answer

$$5 + 18i$$

Answer

$$5 + 6i $$

Answer

$$6 + 18i$$

Answer

$$8 + 15i$$

Question 3

If $$5x + i (4x – y) = 2 + i (– 6)$$, where $$x$$ and $$y$$ are real numbers, then find the values of $$x$$ and $$y$$.

Accepted Answer

$$x = \dfrac{2}{5}$$ and y = $$\dfrac{38}{5}$$

Answer

$$x = \dfrac{2}{5}$$ and y = $$\dfrac{28}{5}$$

Answer

$$x = \dfrac{5}{2}$$ and y = $$\dfrac{28}{5}$$

Answer

$$x = \dfrac{2}{5}$$ and y = $$\dfrac{5}{38}$$

Question 4

Express $$(-\sqrt{2}+\sqrt{-3}) (3\sqrt{2} - 	ext{i})$$ in the form of $$a + ib$$.

Accepted Answer

$$(-6+\sqrt{3})+\sqrt{2}(1+3\sqrt{3})i$$

Answer

$$(-6+\sqrt{3})+\sqrt{2}(1+2\sqrt{3})i$$

Answer

$$(-6+\sqrt{2})+\sqrt{2}(1+2\sqrt{3})i$$

Answer

$$(-6+\sqrt{2})+\sqrt{2}(1+3\sqrt{3})i$$

Question 5

Find the multiplicative inverse of the complex number $$\sqrt{3}+5i$$

Accepted Answer

$$\dfrac{\sqrt{3}}{28}-\dfrac{5i}{28}$$

Answer

$$\dfrac{\sqrt{5}}{28}-\dfrac{8i}{28}$$

Answer

$$\dfrac{\sqrt{5}}{23}-\dfrac{3i}{23}$$

Answer

$$\dfrac{\sqrt{5}}{28}-\dfrac{3i}{28}$$