# Online Algebra Tutoring: Complex Numbers (Division)

## Algebra Worksheets

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### Learn Multiplication & Division of Complex Numbers from Certified Online Algebra Tutor

**3. **Multiplication

We use FOIL Method (which we use to multiply two binomials) to multiply two complex numbers.

**F = Firsts**

**O = Outers**

**I = Inners**

**L = Lasts**

i = √-1, i^{2} = -1, i^{3} = – i, i^{4} = 1

p+qi and r+ti are two complex numbers.

(p+qi ) ×(r+ti) = pr + pti + qir + qti^{2}

pr + (pt+qr) i + qti^{2}

* Example:* (6 + 3i) × (3 + 4i)

= 18 + 24i + 9i + 12i^{2}

= 18 + (24 + 9) i + 12(-1) ———— (because i2 = -1)

= 18 + 33i – 12

= 6+ 33

**4. **Division

p+qi is a complex number. p-qi is the conjugate of p+qi. We can use conjugates to divide two Complex Numbers.

**Method:**

To divide two Complex Numbers, multiply numerator and denominator by the conjugate of the denominator.

**The numerator and denominator can be solved by using FOIL.**

(r+ti)×(r-ti) =r^{2}-rti + rti-t^{2} i^{2}

r^2-t^{2} (-1)

r^2+t^{2}

**Example:** (2+4i)÷ (3-4i)

Conjugate of 3 – 4i is 3 + 4i, so multiplying the numerator and denominator by this conjugate.

## Check point:

1. (3 – 3i) × (2 + 4i)

2. (6 – 3i)÷(2 + i)

3. (7 + 3i) ÷ (2 + 5i)

4. (4 + 5i) ÷ (3 + 2i)

5. (2 – 3i) × (4 + 7i)

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Understanding graphs, charts, and opinion polls in a newspaper, for calculating house and car payments, and for choosing a long-distance telephone service are impossible without strong math skills …and the only way to develop strong math skills is by constant practice.

‘Practice makes a man perfect’ holds true for no other field better than for math. A middle or high school student must set aside a minimum of an hour for math every day. Other than textbooks, worksheets help you revise and understand concepts better.

Our expert tutors prepare online maths worksheets that are age and grade-appropriate. Grade-wise math worksheets for Elementary Math, Arithmetic, Pre-Algebra, Algebra, Geometry, Trigonometry, Statistics, Pre-Calculus and Calculus can be solved to improve math skills, to get ahead or to even catch up.

You may download these FREE online math worksheets in the PDF format, and then print and email us their solutions for a free evaluation and analysis by eTutorworld’smath expert tutors.

You may solve these worksheets by yourself or with your peers while studying together.

The Answer Key at the end of each worksheet allows for a self-evaluation.

## Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12, Test Prep help for Standardized tests like SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a **FREE CLASS.**

*No credit card required, no obligation to purchase. **Just book a free class to meet a tutor and get help on any topic you want!*

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