Express the given complex number in the form a + ib:

Express the given complex number in the form a + ib: i⁹ + i¹⁹

Express the given complex number in the form a + ib: 3(7 + i7) + i(7 + i7)

Express the given complex number in the form a + ib ,  (1 – i) – (–1 + i6)

Express the given complex number in the form a + ib:

Express the given complex number in the form a + ib:

Express the given complex number in the form a + ib:  (1 – i)⁴

Express the given complex number in the form a + ib:

Express the given complex number in the form a + ib:

Find the multiplicative inverse of the complex number 4 – 3i

Find the multiplicative inverse of the complex number 

Find the multiplicative inverse of the complex number –i

Find the modulus and the argument of the complex number

Find the modulus and the argument of the complex number

Convert the given complex number in polar form: 1 – i

Convert the given complex number in polar form: – 1 + i

Convert the given complex number in polar form: – 1 – i

Convert the given complex number in polar form: –3

Convert the given complex number in polar form: 

Convert the given complex number in polar form: i

Solve the equation x² + 3 = 0

Solve the equation 2x² + x + 1 = 0

Solve the equation x² + 3x + 9 = 0

Solve the equation –x² + x – 2 = 0

Solve the equation x² + 3x + 5 = 0

Solve the equation x² – x + 2 = 0

Solve the equation 

Solve the equation 

Solve the equation

Solve the equation 

Evaluate: 

For any two complex numbers z₁ and z₂, prove that

Re (z₁z₂) = Re z₁ Re z₂ – Im z₁ Im z₂

Convert the following in the polar form:

(i) , (ii) 

Solve the equation

Solve the equation

Solve the equation 27x² – 10x + 1 = 0

Solve the equation 21x² – 28x + 10 = 0

If a + ib =, prove that a² + b² =