Modulus and Argument (Degrees) to Rectangular Form (Level 1)

This math topic focuses on converting complex numbers from polar (modulus and argument in degrees) to rectangular form. Each question presents a specific complex number in polar coordinates (r, θ) and asks to identify the correct rectangular form (a + bi) among multiple choices. This exercise enhances understanding of the relationship between polar and rectangular forms of complex numbers and requires knowledge of trigonometry to compute the cosine and sine of the given angles for the conversion.

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Complex Numbers - Modulus and Argument (Degrees) to Rectangular Form Worksheet

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Math worksheet on 'Complex Numbers - Modulus and Argument (Degrees) to Rectangular Form (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (5, 307 to the power of \ circ)
a A LaTex expression showing 2 + 6i
b A LaTex expression showing 2 + 4i
c A LaTex expression showing 2 - 6i
d A LaTex expression showing 1 - 4i
e A LaTex expression showing 1 + 4i
f A LaTex expression showing 3 - 4i
2
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (6.3, 288 to the power of \ circ)
a A LaTex expression showing -6i
b A LaTex expression showing 1 - 6i
c A LaTex expression showing 1 + 6i
d A LaTex expression showing 2 + 6i
e A LaTex expression showing 6i
f A LaTex expression showing 2 - 6i
3
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (5.8, 149 to the power of \ circ)
a A LaTex expression showing -4 - 3i
b A LaTex expression showing -4 - 4i
c A LaTex expression showing -6 - 4i
d A LaTex expression showing -6 - 3i
e A LaTex expression showing -5 - 3i
f A LaTex expression showing -5 + 3i
4
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (3.6, 56 to the power of \ circ)
a A LaTex expression showing 4i
b A LaTex expression showing 2 + 3i
c A LaTex expression showing 2 + 2i
d A LaTex expression showing 2 + 1i
e A LaTex expression showing 3i
f A LaTex expression showing -4i
5
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (5, 323 to the power of \ circ)
a A LaTex expression showing 3 - 3i
b A LaTex expression showing 4 - 3i
c A LaTex expression showing -2 + 5i
d A LaTex expression showing 2 - 3i
e A LaTex expression showing -2 + 6i
f A LaTex expression showing -2 + 3i
6
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (7.1, 315 to the power of \ circ)
a A LaTex expression showing 5 - 3i
b A LaTex expression showing 5 - 5i
c A LaTex expression showing 6 + 3i
d A LaTex expression showing -6 + 3i
e A LaTex expression showing -8 + 3i
f A LaTex expression showing 6 - 3i
7
Find the rectangular form of the complex number that has a modulus and argument (r, θ) of
A LaTex expression showing (6.7, 297 to the power of \ circ)
a A LaTex expression showing 3 - 8i
b A LaTex expression showing 3 + 9i
c A LaTex expression showing 3 - 6i
d A LaTex expression showing 6 + 9i
e A LaTex expression showing 3 + 8i
f A LaTex expression showing 4 + 9i