How to divide complex numbers

Practice Questions

PSAT Math › How to divide complex numbers

Questions

9

1

Define an operation $\ast$ as follows:

For all complex numbers ,

$a \ast b = \frac{ai}{b}$ .

Evaluate $(2+ i) \ast (2-i)$ .

2

Simplify by rationalizing the denominator:

$\frac{15i}{4- 3i}$

3

Simplify by rationalizing the denominator:

$\frac{2+3i}{4+ 3i}$

4

Define an operation $\ast$ as follows:

For all complex numbers ,

$a \ast b = \frac{ a^{3}}{b^{3} + 1}$

Evaluate $i \ast i$ .

5

Define an operation $\ast$ as follows:

For all complex numbers ,

$a \ast b = \frac{ab}{i}$ .

Evaluate $(3+ 4i) \ast (4-3i)$ .

6

Divide:

$-100 \div 5i$

7

Simplify by rationalizing the denominator:

$\frac{ 25- 12i}{ - 10i}$

8

Simplify by rationalizing the denominator:

$\frac{ 21i}{3+ i\sqrt{5}}$

9

Simplify by rationalizing the denominator:

$\frac{20 + 6i}{8i}$

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