Free Printable polar and complex forms

1.

convert from rectangular to polar:

(-1, -4) -->

a)

$\left(\sqrt{17},\ 256\degree\right)$

b)

$\left(4.1,104\degree\right)$

c)

$\left(\sqrt{17},76\degree\right)$

d)

$4.1\left(\cos76\degree+i\sin76\degree\right)$

2.

convert from polar to rectangular:

$\left(10,-\frac{\pi}{5}\right)$ -->

a)

$\left(10,\ -0.628\right)$

b)

$\left(8.1,-5.9\right)$

c)

$\left(10,-0.11\right)$

d)

$\left(10,36\right)$

3.

convert from standard form to polar complex:

4+3i -->

a)

$5\left(\cos53\degree+i\sin53\degree\right)$

b)

$5\left(\cos37\degree+i\sin37\degree\right)$

c)

$5\left(\cos42\degree+i\sin42\degree\right)$

d)

$\sqrt{5}\left(\cos37\degree+i\sin53\degree\right)$

4.

convert from standard form to polar form:

$y=\frac{1}{2x}$ -->

a)

$r=\frac{1}{\sqrt{\sin2\theta}}$

b)

$r=\frac{1}{\sqrt{\cos2\theta}}$

c)

$r=2\cot\theta$

d)

$r=\frac{1}{2\cos\theta-\sin\theta}$

5.

convert from standard form to polar form:

$x^2+\left(y-3\right)^2=9$ -->

a)

$r=6\csc\theta$

b)

$r=6\sin\theta$

c)

$r=6\cos\theta$

d)

$r=6\sec\theta$

6.

given: 27.6 + 23.1i = $36\left(\cos40\degree+i\sin40\degree\right)$

which answer below is NOT a solution for:

\sqrt{27.6+23.1i}

you may select more than one choice if applicable

a)

$\sqrt{36}\left(\cos20\degree+i\sin20\degree\right)$

b)

$6\left(\cos220+i\sin220\right)$

c)

$-5.6-2.1i$

d)

$\left(2.6,\ 5.1\right)$

7.

given: 88.4 + 88.4i = $125\left(\cos45\degree+i\sin45\degree\right)$

which answer below is NOT a solution for the cube root of:

88.4+88.4i

you may select more than one choice if applicable

a)

$25\left(\cos45\degree+i\sin45\degree\right)$

b)

$5\left(\cos203+i\sin203\right)$

c)

$-1.3-4.8i$

d)

$-3.54i+3.54i$

8.

given: 2.74 + 7.52i = $8\left(\cos70\degree+i\sin70\degree\right)$

which answer below is the correct solution for:

\left(2.74+7.52i\right)^4

a)

$\left(2.74\right)^4+\left(7.52\right)^4i$

b)

$32\left(\cos280\degree+i\sin280\degree\right)$

c)

$711-4034i$

d)

$8^4\left(\cos\left(70^4\degree\right)+i\sin\left(70^4\degree\right)\right)$

9.

given: 2.74 + 7.52i = $8\left(\cos70\degree+i\sin70\degree\right)$ and

27.6 + 23.1i =

36\left(\cos40\degree+i\sin40\degree\right)

which answer below is a solution for: (2.74 + 7.52i)(27.6+23.1i)

a)

$-12.3+33.8i$

b)

$44\left(\cos110\degree+i\sin110\degree\right)$

c)

$0.22\left(\cos30\degree+i\sin\degree\right)$

d)

$-98.5+270.6i$

10.

given: a = $3\left(\cos150\degree+i\sin150\degree\right)$ and b = $2\left(\cos30\degree+i\sin30\degree\right)$ which answer below is a solution to a+ b?

a)

$6\left(\cos180+i\sin180\right)$

b)

$-5$

c)

$\sqrt{7}\left(\cos109\degree+i\sin109\degree\right)$

d)

$-0.9+2.5i$

polar and complex forms

Total questions: 10

Worksheet time: 38mins

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