Question

if z=2+3i and w=5-4i show that zw bar= z bar w bar​

Answer 1

Answer:

1 Complex Numbers

1.1 Algebra of Complex Numbers

The number i is declared by law to satisfy the equation

i

2 = −1.

A complex number is an expression of the form x + yi, with x and y real

numbers. Complex numbers are added, subtracted, and multiplied as with

polynomials. Examples

(2 + 3i) + (5 − 6i) = 7 − 3i.

(2 + 3i) − (5 − 6i) = −3 + 9i.

(2 + 3i)(5 − 6i) = 10 + 15i − 12i − 18i

2 = (10 + 18) + i(15 − 12) = 28 + 3i.

Division is trickier. Observe that

(2 − 3i)(2 + 3i) = 4 + 9 + 6i − 6i = 13.

That means that

13

2 + 3i

= 2 − 3i.

Divide both sides by 13:

1

2 + 3i

=

2 − 3i

13

.

In general,

1

a + bi =

a − bi

a

2 + b

2

.

Now for division

5 − 6i

2 + 3i

= (5 − 6i) ×

1

2 + 3i

=

(5 − 6i) ×

2 − 3i

13

=

(5 − 6i)(2 − 3i)

13

= −8/13 − 27/13i.

Problems: Compute A + B and A − B and AB and A/B for

• A = 2i and B = 1 − i.

• A = 1 + 2i and B = 4 − 3i

• A = 2 − 5i and B = −2 + 7i

Step-by-step explanation: