Polar Form of Complex Numbers
Write the number in polar form:
1
1
z1 * z2 = ?
where z1 = cos (pi/2) + isin (pi/2) and
z2 = cos (pi) + isin(pi)
-2i
z1 / z2 = ?
where z1 = cos (pi/2) + isin (pi/2) and
z2 = 0.5(cos (pi/4) + isin(pi/4))
((2)^1/2)/4 + i(2^1/2)/4
Find all the roots of:
x^4 - 1 = 0
1, -1, i, -i
Write the number in polar form:
i
i
z1 * z2 = ?
where z1 = 3(cos (pi/4) + isin (pi/4)) and
z2 = 6(cos (pi) + isin(pi))
9(2^1/2) - 9i(2^1/2)
z1 / z2 = ?
where z1 = 3(cos (pi) + isin (pi)) and
z2 = 8(cos (pi/2) + isin(pi/2))
(3/8)i
Find all the roots of:
x^4 + 1 = 0
(2^1/2)/2 + [i(2^1/2)/2]
-(2^1/2)/2 + [i(2^1/2)/2]
(2^1/2)/2 - [i(2^1/2)/2]
-(2^1/2)/2 - [i(2^1/2)/2]
Write the number in polar form:
1 - i
2^1/2 - i(2^1/2)
z1 * z2 = ?
where z1 = 1.5(cos (-pi/3) + isin (-pi/3)) and
z2 = (9/4)(cos (-pi) + isin(-pi))
(-27/16) + (27i(3^1/2) /16)
z1 / z2 = ?
where z1 = 2(cos (pi/3) + isin (pi/3)) and
z2 = 0.5(cos (-pi/6) + isin(-pi/6))
4i
Find all the roots of:
x^2 + 1 = 0
i(2^1/2), -i(2^1/2)
Write the number in polar form: (Do not simplify the trig functions)
-4 - 3i
5[cos(0.643) + isin(0.643)]
z1 * z2 = ?
where z1 = 7(cos (pi/4) + isin (pi/4)) and
z2 = 18(cos (-pi/3) + isin(-pi/3))
121.706 + 32.611i
z1 / z2 = ?
where z1 = (1/8)cis(pi/4) and
z2 = (0.25)cis(pi/3)
0.482 - 0.129i
Find all the roots of:
x^5 - 1024 = 0
4, 1.236 + 3.804i, -3.236 + 2.351i,
-3.236 - 2.351i, 1.236 - 3.804i
Write the number in polar form: (Do not simplify the trig functions)
-7 + 6.5i
9.552(cos(-0.748) + isin(-0.748))
z1 * z2 = ?
where z1 = 5cis(7pi/4) and
z2 = 86cis(3pi)
-215(2)^1/2 + 215i(2^1/2)
z1 / z2 = ?
where z1 = 0.75cis(2pi/3) and
z2 = 1.6cis(4pi)
-15/64 + 15i(3^1/2)/64
Find all the roots of:
x^6 + 117649 = 0
7i, -7i, 7(3^1/2)/2 + 7i/2, -7(3^1/2)/2 + 7i/2,
-7(3^1/2)/2 - 7i/2, 7(3^1/2)/2 - 7i/2