Question

Find the modulus
of (1-i) (-3+3i)​

Answer 1

Answer: 6

Given a complex number as a product of two complex numbers, we have to find the modulus of the resulting complex number.

First let's find the resulting complex number,

⇒ (1 - i)(-3 + 3i)

⇒ (1 - i)(3i - 3)

⇒ 1×3i - 1×3 - 3i×i - i×-3

⇒ 3i - 3 - 3i² + 3i

⇒ 6i - 3 - 3×-1

⇒ 6i - 3 + 3

⇒ 6i + 0

Here,

• Real part = 0
• Imaginary part = 6

Now, we know, modulus of a complex number Z = x + iy is given by,

• |Z| = √( x² + y² )

Where, x and y are the real and imaginary parts respectively.

So,

⇒ Modulus of given Z = √( 0² + 6² )

⇒ Modulus of given Z = √6²

⇒ Modulus of given Z = 6

Hence, The modulus of the given complex number which is expressed as the product of two complex numbers is 6 .

Answer 2

$\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}$

( 1 - i )( -3 + 3i )

= ( 1 - i )( 3i - 3 )

= 1×3i - 1×3 - 3i×i - ix-3

= 3i - 3 - 3i² + 3i

= 6i - 3 - 3 × -1

= 6i - 3 + 3

= 6i + 0

Here,

Real Part = 0

Original Part = 6.

Now, We know Modules of Complex Number,

z = x + iy is given by,

|Z| = root(x² + y²)

So,

Module of given Z = root( 0² + 6² )

= root6²

= 6

• I Hope it's Helpful My Friend.