Calculate (3+2i)+(5−4i) and (8−3i)−(2+7i).

A) 7 - 3i and 5 - 11i

B) 7 + 3i and 5 + 11i

C) 8 - 2i and 6 - 10i

D) 7 + 2i and 5 + 11i

Convert each number to polar form. \$ (sqrt(2) + i sqrt(2))^8 \$

A) 253

B) 254

C) 255

D) 256

Convert \$ 10cis(pi/3) \$ to rectangular form.

A) \$ 5 + (5i(\sqrt 3)) \$

B) \$ 5 + (5i(\sqrt 3)) \$

C) \$ 5 + (5i(\sqrt 3)) \$

D) \$ 5 + (5i(\sqrt 3)) \$

Find the product of \$ z1 = 12 cis((2pi)/3) \$ and \$ z2 = 10 cis((3pi)/4) \$

A) \$ 120 cis((17pi)/12) \$

B) \$ 120 cis((11pi)/12) \$

C) \$ 110 cis((17pi)/12) \$

D) \$ 150 cis((15pi)/12) \$

Given \$ z = 8 - 8i(\sqrt(3)) \$, compute \$ z^2 \$.

A) \$ -128 - 128i(\sqrt(3)) \$ ​

B) \$ -118 - 128i(\sqrt(3)) \$ ​ ​

C) \$ -128 - 128i(\sqrt(5)) \$

D) ​\$ -128 - 108i(\sqrt(2)) \$

Suppose \$z = (2 - i)^2 + ((7 - 4i) / (2 + i)) - 8\$, express z in the form of x + iy such that x and y are real numbers.

A) z = (-2 - 7i)

B) z = (-3 - 7i)

C) z = (2 + 7i)

D) z = (2 - 7i)

If \$z_1 = 2 + 8i\$ amd \$z_2 = 1 - i\$, then find \$|z_1 / z_2|\$.

A) \$\sqrt(4)\$

B) \$\sqrt(34)\$

C) \$\sqrt(30)\$

D) \$\sqrt(44)\$

If \$|z^2 - 1| = |z^2| + 1\$, then show that z lies on an imaginary axis.

A) Doesn’t exists any axis.

B) z lies on the x axis.

C) z lies on the y axis.

D) z lies on the no axis.

Find real x and y if (x - iy) (3 + 5i) is the conjugate of – 6 – 24i.

A) x = 3 and y = 3

B) x = 2 and y = -2

C) x = 3 and y = -3

D) x = -2 and y = 2

Find the relation between a and b if z = a + ib if \$|(z - 3)/(z + 3)| = 2\$.

A) \$(a + 5)^2 + (4^2) = (b^2)\$

B) \$(4 + 5)^2 + (a^2) = (b^2)\$

C) \$(a + 5)^2 + (7^2) = (3^2)\$

D) \$(a + 5)^2 + (b^2) = (4^2)\$