Complex Numbers - Polar Form (Radians) to Rectangular Form (Level 1)

This math topic focuses on converting complex numbers from polar form (using radians) to rectangular form. It includes problems that require transforming expressions of the type \( r(\cos(\theta \text{ rad}) + i \sin(\theta \text{ rad})) \) into the form \( a + bi \), where \( r \) is the magnitude, \( \theta \) is the angle in radians, \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit. The worksheet provides multiple choice answers for each problem, testing the student's ability to accurately perform these conversions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Polar Form (Radians) to Rectangular Form

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.


Find the rectangular form of this polar form complex number

7.2(cos(0.8π  rad)+isin(0.8π  rad))7.2(cos(0.8 \pi\;rad) + i \cdot sin(0.8 \pi\;rad))

Complex Numbers - Polar Form (Radians) to Rectangular Form Worksheet

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Math worksheet on 'Complex Numbers - Polar Form (Radians) to Rectangular Form (Level 1)'. Part of a broader unit on 'Complex Numbers' Learn online: app.mobius.academy/math/units/complex_numbers/
1
A LaTex expression showing 8.5(cos(1.3 Pi \;rad) + i times sin(1.3 Pi \;rad))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -4 + 11i
b A LaTex expression showing -6 - 8i
c A LaTex expression showing -6 + 11i
d A LaTex expression showing -6 + 10i
e A LaTex expression showing -6 - 10i
f A LaTex expression showing -6 - 6i
2
A LaTex expression showing 7.1(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
Find the rectangular form of this polar form complex number
a A LaTex expression showing 5 + 5i
b A LaTex expression showing -6 + 4i
c A LaTex expression showing -5 + 3i
d A LaTex expression showing 5 + 4i
e A LaTex expression showing -6 + 3i
f A LaTex expression showing 5 + 3i
3
A LaTex expression showing 5(cos(1.3 Pi \;rad) + i times sin(1.3 Pi \;rad))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -1 - 6i
b A LaTex expression showing -3 - 6i
c A LaTex expression showing -3 - 8i
d A LaTex expression showing -1 - 5i
e A LaTex expression showing -1 - 8i
f A LaTex expression showing -3 - 4i
4
A LaTex expression showing 5.4(cos(1.6 Pi \;rad) + i times sin(1.6 Pi \;rad))
Find the rectangular form of this polar form complex number
a A LaTex expression showing 2 - 5i
b A LaTex expression showing -2 - 8i
c A LaTex expression showing -2 - 10i
d A LaTex expression showing 2 - 7i
e A LaTex expression showing -2 - 9i
f A LaTex expression showing -2 - 7i
5
A LaTex expression showing 3.6(cos(0.8 Pi \;rad) + i times sin(0.8 Pi \;rad))
Find the rectangular form of this polar form complex number
a A LaTex expression showing -4 + 3i
b A LaTex expression showing -2 + 5i
c A LaTex expression showing -4 + 2i
d A LaTex expression showing -2 + 4i
e A LaTex expression showing -3 + 2i
f A LaTex expression showing -4 + 5i
6
A LaTex expression showing 4.2(cos(0.8 Pi \;rad) + i times sin(0.8 Pi \;rad))
Find the rectangular form of this polar form complex number
a A LaTex expression showing 1 + 4i
b A LaTex expression showing -1 + 3i
c A LaTex expression showing -3 + 3i
d A LaTex expression showing -2 + 3i
e A LaTex expression showing -1 + 4i
f A LaTex expression showing 1 + 5i
7
A LaTex expression showing 6.4(cos(0.3 Pi \;rad) + i times sin(0.3 Pi \;rad))
Find the rectangular form of this polar form complex number
a A LaTex expression showing 4 + 5i
b A LaTex expression showing -1 + 5i
c A LaTex expression showing 1 + 5i
d A LaTex expression showing -1 - 5i
e A LaTex expression showing -2 + 5i
f A LaTex expression showing 3 + 5i