## HOW TO ADD SUBTRACT MULTIPLY AND DIVIDE COMPLEX NUMBERS

How to Add Subtract Multiply and Divide Complex Numbers ?

Here we are going to see, how to add, subtract, multiply and divide complex numbers.

Addition and subtraction of complex numbers :

Suppose a, b, c, and d are real numbers. Then

• (a + bi) + (c + di) = (a + c) + (b + d)i
• (a + bi) − (c + di) = (a − c) + (b − d)i

Multiplying complex numbers :

Suppose a, b, c, and d are real numbers. Then,

• (a + bi)(c + di) = (ac − bd) + (ad + bc)i

Division of complex numbers :

Suppose a, b, c, and d are real numbers, with c + di  0. Then (a + bi)/(c + di)

=  [(ac + bd) / (c2 + d2)] + [(bc − ad)(c2 + d2) i]

## How to Add Subtract Multiply and Divide Complex Numbers - Examples

Write the expression in the form a + bi, where a and b are real numbers.

Question 1 :

(4 + 2i) + (3 + 8i)

Solution :

=  (4 + 2i) + (3 + 8i)

=  (4 + 3) + (2i + 8i)

=  7 + 10i

Question 2 :

(5 + 7i) + (4 + 6i)

Solution :

=  (5 + 7i) + (4 + 6i)

=  (5 + 4) + (7i + 6i)

=  9 + 15i

Question 3 :

(5 + 3i) − (2 + 9i)

Solution :

=  (5 + 3i) − (2 + 9i)

=  5 + 3i - 2 - 9i

=  3 - 6i

Question 4 :

(9 + 2i) − (6 + 7i)

Solution :

=  (9 + 2i) − (6 + 7i)

=  9 + 2i - 6 - 7i

=  3 - 5i

=  3 - 6i

Question 5 :

(9 + 2i) − (6 + 7i)

Solution :

=  (9 + 2i) − (6 + 7i)

=  9 + 2i - 6 - 7i

=  3 - 5i

Question 6 :

(8 − 4i)(2 − 3i)

Solution :

= (8 − 4i)(2 − 3i)

=  16 - 24i - 8i + 12i2

=  16 - 32i + 12(-1)

=  16 - 12 - 32i

=  4 - 32i

Question 7 :

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

Solution :

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

=  (1 + 2i)(3 - 4i)/(3 + 4i)(3 - 4i)

=  (3 - 4i + 6i - 12i2)/(32 - 16i2)

=  (3 + 2i + 12)/(9 + 16)

=  (15 + 2i)/25

Question 8 :

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

Solution :

=  (4 + 3i)/(5 - 2i)

=  (4 + 3i)(5 + 2i)/(5 - 2i)(5 + 2i)

=  (20 + 8i + 15i + 6(-1))/(52 - 4i2)

=  (20 + 23i - 6)/(25 + 4)

=  (14 + 23i)/29

After having gone through the stuff given above, we hope that the students would have understood "How to Add Subtract Multiply and Divide Complex Numbers".

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