Find the conjugate of (6 + 5i )²

2

(a)

Simplify the following
(2i)³

2

(a)

Express each of these complex numbers in the form a + ib: \(\frac { 1 }{ 1-cos\theta +2i\quad sin\quad \theta } \)

2

(a)

Find the multiplicative inverse of the following complex number 3+2i

2

(a)

Find the multiplicative inverse of the following complex number cos \(\theta \)+i sin \(\theta \)

2

(a)

Find real \(\theta\) such that \(\frac{3+2isin\theta}{1-2isin\theta}\) is purely real.

3

(a)

Solve the quadratic equation 8x² - 9x + 3 = 0.

3

(a)

Solve the quadratic equation 13x²+ 7x + 1 = 0.

3

(a)

Solve the equation 2x²-(3+7i)-(3-9i)=0

3

(a)

Prove that the following complex number is purely real: \(\left[ \frac { 3+2i }{ 2-3i } \right] +\left[ \frac { 3-2i }{ 2+3i } \right] \)

3

(a)

If f(z) = \(\frac { 7-z }{ 1-{ z }^{ 2 } } \) where z= 1 + 2i , then find \(|f(z)|\)

5

(a)

Solve that equation \(\left| z \right| =z+1+2i\).

5

(a)

Convert the complex numbers in polar form \(\sqrt { 3 } +i\)

5

(a)

Solve x²- 2x +\(\frac { 3 }{ 2 } \) = 0

5

(a)

Find the square root of \(-2+2\sqrt {3}i.\)

5

(a)