Right, so I am doing an assignment and I am tasked with this question.
Q) Convert the complex number from the given polar form to the rectangular form x+yj
5(cos20+jsin20)
So if anyone can show me how you get the cartesian form, i'll be happy.
For the answer is 4.70+1.71j
A decent working out will earn you easy 10pts.
Q) Convert the complex number from the given polar form to the rectangular form x+yj
5(cos20+jsin20)
So if anyone can show me how you get the cartesian form, i'll be happy.
For the answer is 4.70+1.71j
A decent working out will earn you easy 10pts.
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5(cos(20°) + j sin(20°))
r = 5
θ = 20°
We know r² = x² + y²
And θ = tan⁻¹(x/y)
tan(θ) = x/y
tan(20°) = x/y
0.36397y = x
r² = x² + y²
5² = (0.36397y)² + y²
y = 4.69846 since we know y > 0 (i.e. 20° ∈ QI)
r² = x² + y²
5² = x² + (4.69846)²
x = 1.71011
So our final result is:
y + j x
4.69846 + j 1.71011
r = 5
θ = 20°
We know r² = x² + y²
And θ = tan⁻¹(x/y)
tan(θ) = x/y
tan(20°) = x/y
0.36397y = x
r² = x² + y²
5² = (0.36397y)² + y²
y = 4.69846 since we know y > 0 (i.e. 20° ∈ QI)
r² = x² + y²
5² = x² + (4.69846)²
x = 1.71011
So our final result is:
y + j x
4.69846 + j 1.71011
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x+jy=5(cos20+jsin20)=5cos20+j5sin20) so calculate 5cos20 and 5sin20.
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x is cosine and y is sine.