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Sladkaya [172]
3 years ago
15

Two complex numbers are given byz1= 3 +j4 andz2= 2 +j3. Determine in both polar andCartesian forms

Mathematics
1 answer:
Marat540 [252]3 years ago
3 0

Answer:

Cartesian

z₁= 3 +4*j

z₂= 2 +3*j

Polar

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)

Step-by-step explanation:

for the complex numbers z the cartesian form of is

z= x + y*j

then

1) z₁= 3 +4*j (cartesian form)

2) z₂= 2 +3*j (cartesian form)

the polar form is

z= r* e^jθ

where

r= √(x²+y²) → r₁ = √(3²+4²) = 5 ,  r₂ = √(2²+3²) = √13

and

θ = tan⁻¹ (y/x)  → θ₁  = tan⁻¹ (4/3)= 0.927 rad , θ₂  = tan⁻¹ (3/2)= 0.982 rad

then

z₁=5 * e^ (0.927*j)

z₁=√13 * e^ (0.982*j)

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At the beginning of an environmental study, a forest covered an area of 1500km^2. Since then, the area has decreased by 6.3% eac
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The <em><u>correct answer</u></em> is:

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An exponential function is of the form

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For our problem, a, the initial population, is 1500.

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3 years ago
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Answer: choice A) 7017

==========================================================

Work Shown:

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The common difference is d = 7

The nth term formula we'll use is
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The 1000th term corresponds to n = 1000

Replace every n with 1000
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