Exercise 5.1 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: i^–39

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

Express the following expression in the form of a + ib.

Exercise 5.2 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 z₁Re z₂ – Im z₁ Im z₂

Reduce to the standard form.

If x – iy = prove that .

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

Iffind.

If a + ib = , prove that a2 + b2 =

Let.Find (i),(ii)

Find the modulus and argument of the complex number .

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

Find the modulus of .

If (x + iy)3 = u + iv, then show that .

If a and ß are different complex numbers with = 1, then find .

Find the number of non-zero integral solutions of the equation .

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a² + b²) (c² + d²) (e² + f²) (g² + h²) = A² + B².

If , then find the least positive integral value of m.