Mathematics complex numbers help
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Mathematics complex numbers help

[From: ] [author: ] [Date: 12-01-29] [Hit: ]
A decent working out will earn you easy 10pts.0.5² = (0.y = 4.69846 since we know y > 0 (i.e.......
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.

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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

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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.
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