Simplify the expression 2+3i/4+3i

17+6i

25

Step-by-step explanation:

2+3i

4+3i

We want to multiply by the complex conjugate of the denominator

4+3i has a complex conjugate of 4-3i

2+3i             4-3i

*

4+3i           4-3i

Lets multiply the numerator

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

2*4 +4*3i -3i*2 - 3i*3i =

8 +12i -6i - 9i^2

Remember i^2 = -1

8 +6i -9(-1)

17 +6i

Lets multiply the denominator

(4+3i) ( 4-3i)

4*4 +4*3i -3i*4 - 3i*3i =

16 +12i -12i - 9i^2

Remember i^2 = -1

16 -9(-1)

25

Putting numerator over denominator

17+6i

25

4.5cm

Step-by-step explanation:

From the information given in the question, we are informed that an airport runway measuring 450 m is drawn to a scale of 1 cm represent 100m, then the length in the drawing will be calculated thus:

Let the length be represented by x. Therefore, we'll have:

1/x = 100/450

Cross multiply

(100 × x) = (1 × 450)

100x = 450

x = 450/100

x = 4.5

Therefore, the length in the drawing is 4.5cm