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Simplify (4 + 7i)(3 + 4i)?
We will use the concept of multiplication of complex numbers.
Answer: We can write the simplified form of (4 + 7i) (3 + 4i) as (-16 + 37i).
Let us proceed step by step
We will express the product (4 + 7i) (3 + 4i) in the form of a + ib, where a is a real number and b is an imaginary number.
Use the distributive property to multiply the complex numbers.
(4 + 7i) (3 + 4i) = 4 × (3 + 4i) + 7i × (3 + 4i)
= 12 + 16i + 21i + 28i2
= 12 + 37i + 28(-1). [ As we know that i = √-1 and i2 = -1]
= 12 - 28 +37i
= -16 + 37i
Therefore, we can write the simplified form of (4 + 7i) (3 + 4i) as (-16 + 37i).