Question

Find the square roots of 4+3i

Answer 1

Answer:

4+3i−−−−−√=a+bi

Squaring both sides

4+3i=(a+bi)2=a2−b2+2abi

So, a2−b2=4 , and

2ab=3⟹b=32a

Plugging it ⟹

4+3i=a2−(32a)2+2a(32a)i

∴

a2−94a2=4

=a4−4a2−9/4=0

a2=92 or −12

a=±32√ or =±i2√

So,

b=±12√ or =±3i2√

4+3i−−−−−√=±(32–√+12–√i)

What is the square root of 4+3i?

What is the square root of -2+3i?

What is the square root of - 4-3i?

What is the square root of 1+4√3i?

What's the square root of 7+24i?

Let z = 4+3i = 5 (4/5 + i3/5)

5 is the module of z = ||z||=42+32−−−−−−√=25−−√=5 .

=>

z=5(45+i.35)

in Ambebraic form :

z=[5;α+2kπ]

For square roots k =0 and 1

=>

z=[5;α+2kπ]

with

α=arcsin(35)

=>

z=[5;α+2kπ]

For square roots k =0 and 1

=>

z√=[5–√;α+kπ]

Two roots

z1−−√=[5–√;\5:alpha2]

And

z2−−√=[5–√;α2+π]

hope it helps.....