How to convert 1- i to polar form?

A complex number is one that is a combination of both real and imaginary numbers. It has two components or parts, the one which consists of only a real number (any fraction, decimal number, radical or integer) is called the real part and the one which consists of iota (i = √(-1)) is called the imaginary part. 

Rectangular Form of A Complex Number

The rectangular form or the standard form of representing a complex number is the most commonly used manner to write a complex number. It is depicted as follows:

z = a + ib,

where a and b are any real numbers(negative or non-negative integers, decimals, fractional numbers, etc.) and i is the imaginary part and i = √(-1). Below given Venn diagram is an example of the real and imaginary part of a complex number.

Polar Form of a Complex Number

Another way of representing a complex number apart from its standard form is called its polar form. The polar form of a complex number uses its modulus (absolute value) as well as an argument as its constituents. The coordinates of the real and imaginary parts of a complex number make up its polar form. For a complex number z = x + iy, the equation of its polar form is written as follows,

z = r(cosθ + isinθ)

Where r is the modulus of the given complex number given by r =  and θ is the argument of the given complex number and is given by tan^-1(y/x) for all x > 0.

How to convert 1- i to polar form?

Solution:

Given: z = 1 – i

Comparing this with z = x + iy, Therefore, x = 1 and y = -1.

Modulus = r = 

Argument = tan^-1{-1/1} = tan^-1{tan(-π/4} = -π/4

Thus, polar form of 1 – i =

Similar Problems

Question 1: Convert 7 – 5i to polar form.

Solution:

Given, z = 7 – 5i

Comparing this with z = x + iy, Hence,  x = 7 and y = -5.

Modulus = r = 

Argument = tan^-1{5/7} = tan^-1{tan(360° – 35.54°} = 324.46°

Thus, polar form of 7 – 5i =

Question 2: Convert 3 + 5i to polar form.

Solution:

Given, z = 3 + 5i

Comparing this with z = x + iy, Therefore, x = 3 and y = 5.

Modulus = r =  = 5.831

Argument = tan^-1{5/3} = 59.036°

Thus, polar form of 3 + 5i = 5.8[cos(59.036°) + isin(59.036°)].

Question 3: Convert 12 + 10i to polar form.

Solution:

Given, z = 12 + 10i

Comparing this with z = x + iy, Therefore, x = 12 and y = 10.

Modulus = r =  = 15.62

Argument = tan^-1{10/12} = 39.8°

Thus, polar form of 12 + 10i = 15.62[cos(39.8°) + isin(39.8°)].

Question 4: Convert 69 + 420i to polar form.

Solution:

Given, z = 69 + 420i 

Comparing this with z = x + iy, Therefore, x = 69 and y = 420

Modulus = r =  = 425.6

Argument = tan^-1{420/69} = 80.67°

Thus, polar form of 69 + 420i = 425.6[cos(80.67°) + isin(80.67°)].

Question 5: Convert 2 + 2i to polar form.

Solution:

Given, z = 2 + 2i.

Comparing this with z = x + iy, Therefore, x = 2 and y = 2

Modulus = r =  = 2.82

Argument = tan^-1{2/2} = tan^-1{tan(π/4} = π/4

Thus, polar form of 2 + 2i =